Punishment Box

Carr: These here spoons, you keep with ya. Any man loses his spoon spends a night in the box. No one will sit in the bunks with dirty pants on. Any man with dirty pants on sittin' on the bunks spends a night in the box. Any man loud-talkin' spends a night in the box. You got questions, you come to me. I'm Carr, the floor-walker. I'm responsible for order in here. Any man don't keep order spends a night in --
Luke: -- the box.
Carr: [to Luke] I hope you ain't gonna be a hard case.

—Cool Hand Luke

Our protagonist is in a Chain Gang prison and has violated one of the Corrupt Hick sheriff's rules. So they send him to the Punishment Box (more commonly, "The Box.") The Box is a small metal shed in the middle of the compound, exposed to sun. They put you in and you are tortured by sweating it out in 120-plus degree heat, basically frying you alive. Unless it's a cold night, in which case you have to keep from freezing to death.

Various forms of this have been an unfortunate Truth in Television (see The Other Wiki for a few examples), which is probably where the trope originates from.

No real life examples, please; The Other Wiki already has a list that we don't need to duplicate here.

Examples of Punishment Box include:

Anime and Manga

In Axis Powers Hetalia, a particular incident similar to this is Played for Laughs. A strip shows Sealand ignoring his "Papa" Sweden and watching TV. Sweden gets a big cardboard box, writes "England" on it, (for some reason) and then sneaks up behind Sealand, and throws the box over him and shakes it with him inside, calling it a "Dambolis" with Sealand saying "Please stop it!". It's even funnier because the strip is presented as a step-by-step of how to make a Dambolis (it will take 3 minutes, it claims).

Film - Animated

In Chicken Run, Ginger is put on a coal bin every time she's caught trying to escape. Like many other scenes in the film, this is an homage to The Great Escape.
Toy Story 3 has Sunnyside's sandbox used for this purpose.
In Despicable Me, orphans who disobey Miss Hattie get put in the Box of Shame.

Film - Live Action

'The box' in Cool Hand Luke is probably the Trope Codifier here.
In The Great Escape, it was The Cooler and it was reserved for attempted escapees. The fact that Steve McQueen's character had been in it so many times, and had survived, led to him being termed The Cooler King.
In Hook, pirates who have failed are put into the "Boo Box", a chest which is also inhabited by several scorpions.
In Matilda, the sadistic headmistress is fond of (among other things) using the "Chokey," a closet lined with massive spikes and blades, thus like an iron maiden in which there is just barely enough room to stand.
The Japanese prison camp in The Bridge on the River Kwai has a metal punishment box that stands outside in the sun. Prisoners don't get any water.
In Stir Crazy, Gene Wilder asks for an extra day in The Box when they come to get him out. He's just Too Kinky to Torture.
Das Experiment, based on the infamous Stanford prison experiment, recycled in Germany.

Literature

Horatio Hornblower: In Mr. Midshipman Hornblower, Hornblower, while being held prisoner in Spain, is placed into a small hole in the ground covered by a grate. The hole has neither room to stand upright or lie down, forcing the prisoner to crouch uncomfortably while exposed to the elements.
- The same hole appears in the Hornblower telefilm The Duchess and the Devil.
In Dragon and Slave by Timothy Zahn, there are sheds that serve this purpose.
Matilda has "Chokey", which is more or less a non-lethal Iron Maiden.
In The Talisman, during the part of the book that takes place in the Sunlight Gardener Home, rule-breakers are sometimes locked in a refrigerator-shaped container simply called "The Box".

Live-Action TV

In Star Trek: Deep Space Nine episode "Paradise", a group of colonists who crash-landed on a planet 10 years ago use the Box as punishment for any transgression.
Kung Fu: Caine finds himself in a two-man Box, and teaches the other man in the box to meditate so as to avoid the torturous aspects of being in the box. The guards & other prisoners are amazed that they're able to leave under their own power instead of being carried out.
The Incredible Hulk episode "The Slam:" David gets put in one. Strangely enough, he doesn't Hulk Out. Another prisoner in the box next door tells him how to survive: find a rock to suck on, put your head in the least exposed place possible, and don't move around.
My Name Is Earl: Earl goes to prison to cover up the fact that Joy really did the crime in question. The prison there has a 2 person "Hot Box;" there's a chain link fence between the two sides of the box, but there's also a hole in the fence big enough to put your arm through.
In the Firefly episode "Jaynestown", Jayne's former partner is kept prisoner in solitary confinement, in a small (looks to be maybe 5 foot by 5 foot) box on stilts in the middle of a swamp.
A The X-Files Monster of the Week episode starts with a guy being punished by going into small shed. The kicker, this was before a major tornado was about to hit. Of course, not only does the guy survive, he somehow becomes an Intangible Man and murders the warden who put him in the shed.
The heroes are subjected to this punishment in The Time Tunnel episode "Devil's Island" when they arrive on the eponymous French Penal Colony and are mistaken for prisoners.
In Seven Days, Frank's background includes several days in such a box while being a captive (a form of interrogation). He never cracked that way, but the project recovered him from a madhouse.
In The Wild Wild West season 2 episode "The Night of the Bottomless Pit", James and Artie go undercover to Devil's Island. James ends up in The Pit - The Box with a deeply-dug floor - as punishment (and to find the man they were looking for).

Magazines

Done in the Mad Magazine parody of Kung Fu (referenced above).

Newspaper Comics

In Dilbert, the Pointy-Haired Boss once threatened to put Dilbert in "the Box" if he didn't work harder. Dilbert asked if "the Box" was bigger than his cubicle.

Video Games

Alpha Centauri has the "punishment sphere", which make the oppressed masses too frightened to ever riot no matter what. For some reason, constructing this city improvement is not on the list of atrocities that will turn the other civilizations against you.
In The Misadventures of Tron Bonne, some servbots sometimes can start not to obey you; when it happens Tron sends them to the punishment chamber (a minigame that basically is about applying Video Game Cruelty Potential on the servbot).

Web Original

Yu-Gi-Oh!: The Abridged Series has a reference to it:

(Tristan says something stupid)
Joey: Do you want to go back in the box?
Tristan: Please don't make me go in there!

Western Animation

King of the Hill: Bobby is put into one of these at a military school. It most assuredly does not break him.

I've slept on a mattress. I've slept on cement. I'm a mattress guy.

On Recess the Box is just a square drawn on the playground floor. T.J. at first laughs it off, but eventually, it breaks him. He overcome this when a random kid ask for him to help find his ball. When TJ was helpless, the kid calls him out, leading TJ to break out his prison.
In an episode of Batman: The Animated Series, An amnesiac Bruce Wayne becomes a captive of a forced labor camp made up of homeless people, owned by a Fat Sweaty Southerner in a White Suit. The main punishment for failure to work is being placed in the box. Being Batman, he regains his memory and breaks out.
Happy Peppy Gary and Happy Peppy Betty on The Fairly OddParents are shown punishing kids by putting them in the "Fun Box", an inhumanely small cage. They even gave it a happy, peppy theme song.
In Tale Spin, Baloo stays at a Thembrian penal colony which he has mistaken for a fitness camp. He is frequently sent to what he calls a "solar-powered sauna."
In the "Boiling Rock" episode of Avatar: The Last Airbender, the titular prison has "The Cooler," a small refrigerated cell designed to contain fire benders. Plays the trope straight in that it's a small, confined box they're put in as punishment, and inverts the effect in that it's a punishment because it's freezing rather than hot.
In Rugrats, "The Big House", Tommy is sent to time-out in a crib after destroying a cat sculpture by accident, which he apologized to the kid as he was arguing with Big Justin. The head of the daycare didn't see what actually happened and punished Tommy, despite the other two workers correctly believing it was by accident. Big Justin learned how Tommy was able to keep calm during the 5-minutes, as most crack after 2.