So apparently they do. I got this answer on another board......
Yes and no. There is a climate control system in the M1A1 and an improved system in the M1A2, but they aren't really effective on a comfort level. According to tankers I've met, It'll keep the temperature from reaching unsafe levels but you're still going to sweat a lot. The largest reason for cooling in the Abrams is for the benefit of the electronics on board. It's got some pretty awesome electronics for targeting and those systems need to be kept moderately cool to prevent wear and damage. Get any computer too hot and it'll fail. Unfortunately, in many cases keeping the computers comfortable is more important than keeping the people happy. So basically, specs say that our tanks have air conditioning but it isn't like the A/C in your car that you can turn up and chill out with. Military vehicles typically just don't carry comfort as a high priority. I think it would be great to get some more cooling in, but engineers argue about increased weight, room for added equipment, electric supply, etc