The same thing was happening to me, except it didnt get so bad that the belt was burnt. im 95% sure that the a/c, heating console is bad and the whole thing will have to be replaced.. I just bouight the car when i had to get mine fixed so i didnt know crap about how to fix them, ne ways, long story short, the dealer will ass rape you, it ended up costing me over 500 bucks.. if you can, find it and put it in yourself. ive done all the work on my car from there on out.
*If your not living on the edge your taking up too much space*