How difficult would it be to convert a regular US-style shower faucet into a thermostat faucet?

I have a regular US-style shower faucet at home which looks like this:

I would like to convert it into a faucet that has a built-in thermostat, so that I could always have the same water temperature while showering. I see various products being sold for adding a thermostat to one's shower (such as this one from Grontherm), but I would rather not buy one if I'm not sure I can install it.

How difficult would it be to add a thermostat to my shower? Do I need a plumber or is it something I can do on my own? I'm open to hiring a plumber, as long as the installation won't require tearing down half the wall to fit in the new faucet.