Is there a through-the-wall A/C that works with external thermostats?
SOME models of the GE AJCMxx, AJCQxx, AJEMxx, or AJEQxx has the ability to wire in a standard 24 VAC "Class 2" thermostat.   It is explained in the manuals, which I believe you can download from GEAppliances.com.  

I wish I'd thought of this myself when I bought my through-the-wall A/C - it's bound to be better than the internal gas-tube thermostat.