This was the same for Bat's '08 Roadster with 11k miles on it at the time.
I fixed it up late last summer, and the burning smell hasn't been back since.
Mine is an 06 roadster . it only had 18500 when we started noticing the burning smell. I just used grey RTV on the covers ( recomended by a friend that is a Chrysler lead tech ) and it has been great since.