Captain Cold and Heat Wave appear as regular enemies of the Flash in the 2014 TV show The Flash, and part of the team of time travelers in Legends of Tomorrow.
They are showed as strongly connected, forming a duo of partners in crime. It is even revealed in the 7th episode that
Heatwave was selected by Rip Hunter as a way to get Captain Cold into the team. This revelation pushes Heatwave to betray the team and Captain Cold to take care of him. Captain Cold then makes the difficult decision to kill his unstable friend.
In an earlier episode of Legends of Tomorrow (the one with Damian Darhk I think), when the plan of the team backfires and things turn to chaos, Heatwave says something along the lines that he is staying only to save his partner and what happened to the other doesn't matter to him.
However, this friendship seems artificial to me. They have completely opposite personalities: Captain Cold is brilliant, well-spoken, well-mannered, cold-blooded and relies on heavy preparation of his heist, whereas Heatwave is obsessive, hot-headed and presented (especially in Legends of Tomorrow) as quite thick. Although very different people can match and goes along well, it feels wrong to me. Especially considering that Captain Cold had been shown to have no problem with using other people, or killing partners that don't follow his finely crafted plans. He has a sense of honor and loyalty, but in specific circumstances (debt to the Flash, loyalty to his sister but not his terrible father).
I am leaded to think that I missed some background information that would explain their relationship. I am looking for information from the TV show, or in lack of it, from the comics.