Thermal Dissonance

"This platform, it should be red-hot, but it is cool to the touch."

—Aqualad, Young Justice

Simply put, an object or person exhibits Thermal Dissonance when it's not the temperature it should be. It's true that some objects have a very low thermal conductivity, but objects subject to Thermal Dissonance don't heat up or cool down no matter how long they spend in a hot or cold environment. They somehow seem able to defy conventional thermodynamics and choose what temperature they want to be, because they're a piece of hyper advanced Phlebotinum, an Ancient Artifact or stranger fare. When touched or held they are either much warmer or colder than the ambient temperature would indicate, with no obvious reason for this temperature difference. A sufficiently powerful Thermally Dissonant object may also be able to change the temperature of its surroundings, freezing an active volcano or melting a glacier if dropped in.

Since temperature doesn't transmit well through visual media, characters who come in contact with the Thermally Dissonant object have to outright state that it's unusually hot, cold, or body temperature. The character will touch the object and either rapidly pull away their hand commenting on it being too hot or cold, or incredulously grab it since it isn't as hot or cold as it should be. If the object is worn or carried, it never changes temperature either.

Examples of Thermal Dissonance include:

Fan Works

Both Azumi Ito and Ms. Aoyama from Desperately Seeking Ranma radiate cold in their presence, but Ms. Aoyama can actively freeze things around her just by standing next to them.

Film

The DeLorean in Back to The Future follows this, though you can see the effect a little bit.
in Spy Kids 3D, they jump into lava, but it's freezing cold
In The Waterboy, Bobby gives Vicky Valencourt a bottle of water that is extremely cold at all times, even though it's kept in a room-temperature environment. Supposedly this is because it was blessed by an Eskimo medicine man.
The machine room door in Forbidden Planet.
The rocketpack from The Rocketeer remains cool even after flight. It's later explained by Howard Hughes that the rocketpack has a double-walled chamber into which the fuel is pumped, cooling the chamber while preheating fuel simultaneously, to Hand Wave the possibility of Toasted Buns.

Literature

This is played both ways with the Slytherin Locket Horcrux in Harry Potter and the Deathly Hallows. It is described as being cold to the touch, yet at one point it burns Harry's chest, leaving him with yet another scar.
In The Lord of the Rings, Gandalf throws the One Ring into the fire to bring out the letters written on it. When he pulls it out, Frodo is surprised that it's not hot. It takes much hotter fire than normal to affect the Ring at all, which is why is has to be brought to Mount Doom to be destroyed.

Live-Action TV

Used in Classic series of Doctor Who where Timelord healing can involve developing a frost on your skin (Jon Pertwee adventure "The Daemons" and "Planet of the Daleks"), the Doctor's inhumanly low body temp also gives him away in the Colin Baker adventure "Mark Of The Rani".
In Farscape, John (human) has a completly different body temperature than the outwardly human Peacekeepers (who have something of a weakness to heat), which gives him away since Scorpius has infrared vision.
In a typical live action Superhero series, such as Batman or |The Flash, someone on a hot day suddenly finds some slick or crusty white material in a non-refrigerated environment and as they are feel it, they say in disbelief, "Ice??" Of course, that means there is a cold themed supervillain on the loose for that story.

Video Games

In Dwarf Fortress, the deepest level of the caverns has some giant mushrooms called nether-caps which have the property of always being cold, to add to their creepyness. Interestingly, this means that it is impossible to set nether-cap logs on fire—they stay just as cold even when they're at the bottom of a pool of magma.
- Quite a lot of creatures have the "fixed body temperature" tag, which does exactly what it says, including Magma Men and Fire Men. Interestingly they can still affect the temperature of other things even while their own stays the same, letting them spontaneously create or destroy and potentially infinite amount of heat.
In Ultima Underworld II, one of the keys is described as feeling "unnaturally cold to the touch".

Real Life

The Earth's thermosphere. It's supposed to be the hottest part of the Earth's atmosphere, but appears freezing cold because there are very few molecules there.
Freezer burns.
Aluminum foil can be safely touched and removed from a baking pan even though the pan itself may be too hot to touch - this is because the foil, being thin, can't store enough thermal energy to cause burns (that is, the foil is cooled so quickly by your skin that it doesn't cause a burn).
The coasts of Northern California may look sunny and bright as early in the year as February. However, the horrific wind chill often forces everyone to keep wearing thick coats.
A thermal tile from the Space Shuttle can be glowing yellow-to-white-hot on the inside, but you can still pick it up with your bare hands because it has extremely poor thermal conductivity.
- This is also why a meteorite that makes it to the ground is still more or less in one piece, rather than splashed. Iron-nickel alloys are the second worst (after titanium and its alloys) heat conductors among metals. While entering Earth's atmosphere does expose it to quite a bit of heat, its surface will melt and be blown away before much heat is transferred to the inner layers. Also, it comes in fast, so if it arrived from the night side, it probably came from outer parts of the system and is still cold, as it wasn't close enough to Sun for long enough to warm up. The impact eats the rest of kinetic energy and can easily produce enough of heat to melt sand into glass, but it's all on surface, too, and may dissipate out faster than in.