Regarding the deleted Snape entry, two points.
One: Regarding his homicidal outburst over Sirius in book 3 as being allegedly defensible because 'he still believes Sirius killed the Potters', that is entirely wrong. Snape's homicidal outburst is occurring during the very same discussion where the Trio is presenting the testimony that shows Sirius' innocence, and Snape is the chief person in charge of arguing that down. And Snape visibly perjures himself during this sequence. The main reason the Trio are not believed is because of Snape's testimony that Sirius Confunded the Trio into believing a false version of events... a statement that Snape cannot possibly be making in good faith because:
a) At no point did he ever actually see Sirius cast a spell on the Trio, so if he claims that he has he is clearly lying. The fact that Snape is unconscious for most of the relevant conversation and not a witness to anything only makes him acting in even more bad faith if he then offers himself as an eyewitness to the authorities while conveniently 'forgetting' to mention that he was actually KO'ed on the floor at the time.
b) As one of the most experienced Legilimens alive, Snape would be entirely capable of detecting if memory-altering magic had been used as the Trio, especially since book 6 mentions that Dumbledore (Snape's Legilimency and Occlumency instructor) did precisely this to Morfin Gaunt in backstory.
So, Snape knows that Sirius is innocent, and does not care. He still hates the man and wants him to die at the hands of the authority, to the point where he deliberately sabotages Sirius' defense with perjured testimony. Sirius' never being able to clear his name is directly traceable to Snape's malicious action. It was as close to an outright murder attempt on Sirius that Snape could ever dare to make while under Dumbledore's supervision.
Two: Regarding Sirius and Snape allegedly cooling off towards each in later books - Snape spends the entirety of book 5 maliciously tormenting Sirius for alleged decisions of Sirius that Snape not only knows weren't actually Sirius' decision but also knows Sirius violently objected to, to the point where Sirius is driven to his death as much by a need to defy Snape's accusations of 'cowardice' and 'hiding in his house' and 'being useless for your grandson' as they are anything else. As for Snape 'checking on Sirius' safety', the detailed discussion of that is on the Order of the Phoenix Headscratchers page, but the short version is thus: there is a delay in transmission of half the night before the Order actually finds out about what's going on with the Ministry Six, seeing as how the kids left Hogwarts at sunset shortly after giving Snape the wordl, and faced an enormously longer travel time to the Ministry of Magic than the Order did from Grimmauld Place. Scotland to London on thestral-back takes hours. London-to-London via Floo, Apparition, or portkey takes seconds. And yet the Six still arrived at the Ministry first before the Order did.
That delay is logically explainable by only one thing; Snape deliberately stalling as long as possible before reporting in. The only reason he could possibly be doing that is trying to set up a disaster. Indeed, you seriously wonder if Snape would ever have bothered to deliver the message were it not for the fact that unless the entire Ministry Six gets killed off that night (which Snape can't accept as an outcome because Harry needs to live at least long enough to finish killing Voldemort) somebody is eventually going to tell Dumbledore they left a message with Snape before leaving Hogwarts, meaning Snape would have to account for not delivering it.
In conclusion, nothing Snape does with Sirius can remotely qualify as 'heart of gold', given that I've seen less hate-filled outright murder attempts.