Crossfire does improve things, but issues are waiting. Noise, heat, extra power, micro-stutter, driver issues
I would move on, buying the 6870 new or used. Then list your 5770 on eBay or something. Search this site and/or google and learn more about the advantage/disadvantage of cfx.
The single most powerful card you can stick in there is always going to be your best bet.
Based on your current system the 6870 is a winner.
I am not saying don`t cfx, afterall it`s your money and time. I am certainly suggesting you read more about what you`re considering. Sure it sounds cool, pick up another 5770 new or used and double your game. Well, that`s what the 6870 is going to do, but with less hassle.
Whatever you decide for gfx, agree with CPU cooler along with at least a couple case fans intake and a couple exhaust