car overheating??

my car (96 camaro rs) is overheating now, after i just bought it a month ago. car was supposedly in great condition, only 75k miles. but anyways, i think i've narrowed it down to a few things. i changed the thermostat yesterday, so thats not the problem. i'm wondering if maybe my cooling fans are not working, and i checked the radiator, and it should be flushed. but do you think the radiator is whats causing this problem? also it overheats only in traffic, when i speed up, it cools down (which is why i think its the cooling fans). any ideas? i dont wanna take it to some shop and pay $80 for a diagnostic.