How can I install a thermostatic shower head in a finished bathroom?
Thermostatic mixing valves control the temperature by adjusting the amount of hot and cold water.  By the time you get to the shower head, you only have one temperature of water to work with, and the only adjustment you can really make is on or off.  So, no, there's no such product to do what you want.

While I was shopping this weekend, I did see a shower head at the store that changed its LED light colors depending on the water temperature.  With something like this there would be a visible indication of the water temp, but it's not going to prevent scalding, or adjust the temperature.

Also, keep in mind that you can often open up the wall behind the shower to access the plumbing while keeping all the tilework in the shower untouched.  That might be an option for you.  If you're lucky and the back of the wall is in a closet, you can install an access panel and avoid drywall work altogether