Why would a 2002 Jeep Grand Cherokee blow cold air on one side and hot air on the other?

This has to do with a faulty "blend air door" which can get stuck in the wrong position. Fixing it requires pulling the dash and replacing the entire sub-assembly. It's expensive, approximetely $500 at most Jeep dealers. As of 01/2004, Chrysler has released an improved set of parts which should be more reliable.