I've noticed that my weapons have been leveling up really fast. Much faster than they should be, in fact. They're at levels that they hadn't reached previously with the heat I've collected doing runs in the Clockworks. Then it hit me:
The weapons that I've equipped go up one level automatically after you've finished a level.
At least, I think this is what is happening.
Check that you don't have any heat amplifiers running for a start. That'll make your heat gained rise. Also, your heat is going up quicker than you think it should be right? I wouldn't complain ^^