My '82 200e Big Red did the same thing...when it was new! I don't think it was well engineered from the factory. The heat issues on mine seemed to come from the very begining of the stock muffler. That part was closest to the plastics.
I now have NOS fenders on it so I am going to have the whole exhaust ceramic coated before it goes back on. I'll let everyone know how it does. It's not cheap but I've heard it works wonders.
1982 Honda 200 ATC E. Big Red. Finished but still looking for a few bits and pieces.
1998 John Deere Gator 6x4. "Big Green".