Will a dirty air filter cause:
-Overheat, engine runs hot...takes a long time to cool off
-Rough idle, doesnt want to idle

Its a 2000 grizzly 600... So what are the symptoms of a dirty filter?

 

a dirty air filter will cause an engine to run rich because it is not getting as much air as before, causes them to run rough, black smoke, although I thought rich ran cooler and lean runs hotter. WHEN IN DOUBT, CLEAN THE DAMN THING!

 

Cleaning it makes a huge difference. I just cleaned it a couple days ago and was riding around. It runs a great deal better, it amazed me.

 

Well said WallSteet, all cloged up, not as much air intake, runs richer. Just like any air filter, car, bike or what not, if it's dirty it won't run worth a darn. Just take a look at it after each ride, yes if it looks dirty to you, clean it.