Punitive damages in Tennessee are rarer than hen's teeth. But that doesn't mean that they shouldn't be sought in appropriate cases - of course they should.
However, it is not enough to simply say: "what the defendant did was bad, real bad" and hope that you can carry the day. Punitive damage cases are aggressively defended and you need to have a good idea of the way defense counsel is going to approach the case.
Here is an article written by Dale E. Hausman of Washington, D.C. His firm represents insurers in insurance coverage matters. The article is titled "An Insurer's Defense Against Punitive Damages Claims," and although it is a little dated on the law it gives you an idea of what you will be facing at trial - and thereafter.