There are beaver ponds further south than the Smokies, at high elevations, which hold trout. I have begun seeing beaver in a few remote areas which have not been there in the past. I am looking forward to them building me some new areas to fish. Like many species in the post-fur age, they are re-establishing their range. We now enjoy some of the oldest-growth forests that anyone has seen in decades if not longer.
I don't think beavers are a bad thing at all. They need controls (predators), of course. But trout and beavers co-existed happily for a very long time before we came and will do so again. Their dams leak, so water warming is not really an issue, provided they build in an area with enough canopy.