My monitor resolution is 1440x900 and I was hoping to upgrade, but while a card such a Radeon 5770 would fit as well as well as upgraded PSU, the problem I have is properly cooling it and my system. I have checked, and their is only one exhaust fan (I believe it is a 92mm) in the bottem rear and no intake fan. In short, the ventilation sucks. So in short, I either need to add more cooling or pick a card that runs cooler. I'm hoping you guys and gals could assist in in this problem. I need something powerful to run SC2, and hopefully max it out as well as run it smoothly, but yet cool enough that I don't have to worry about anything overheating.
Grab a 5750, its slightly lower power and if you get one of the dual slot version with the enclosed cooler it will exhaust its heat out the back rather than back into the case. It will handle SC2 quite well at that resolution, i have a 4850 and a PII 955 that handles 1920x1080 quite well.
The HD5770 is pretty low power. Power used directly translates into the amount of heat given off by the card. I don't think it should give you a problem but to be safe you may want to get one with an enclosed cooler that vents outside the case. To be extra safe get an HD5750 like hunter mentioned as it uses even less power.
I've read that the Radeon 5770 can run as hot as 80 Degrees Celsius. Although that was with weak cooling like what I will have. Can suggest one of these enclosed cooler cards that vent outside the case? I have no idea how that would look like. I'd like to take a look at those.
Looking at your case I don't think it will be an issue at all. BTW core temperature is another issue entirely from how much heat the card produces. As I said earlier heat is directly related to the amount of power the card uses and all HD5770s are going to use the same power. Core temperature on the other hand just measures how efficiently the cooler manages to remove the heat produced from the GPU processor itself.
As for the card, yes, that is what you are looking for and would be a good choice.