My kenmore dryer has a burning smell. I also have a catching issue with clothes and a thumping noise that I was recommended to replace the felt linter and rear drum support shaft (http://forum.appliancepartspros.com/dryer-repair/566966-kenmore-dryer-thumping-catching-items.html). I still have yet to do it so i wonder if it is a related issue. I am also looking to go ahead and replace the belt since I will be taking the dryer apart. Is the burning a related issue or is there something else I should be looking to replace when I do it?
They used to make a nice kit for the rear "ball" bearing on these. It included everything you needed plus the grease.
He gave you some good advice. The burning might be lint collecting around the heating element. You just need to get in there and check it out.