Why does my mixer shower run intermittently cold?
You seem to be describing an anti-scalding device that is malfunctioning. This could either be a thermostatic valve (as you mention) or a pressure balance valve (another type of anti-scald device).
They have been required by code for many years and while I cannot specifically tell if your shower valve has an anti-scald device in it, given that it looks newer it likely has one.
You should see some sort of manufacturer name on the shower valve. Just Google every single word you see on your shower valve. Also try &quot;Google Image Search&quot; and flip through the images until you see something that looks like your valve.
Googling will help you find the specific valve and see if you can replace the internal anti-scald device. These are often accessible from the front so if you're lucky, you will not need to break through the wall.