Definitely a warranty claim. It would have been best to notice this when you tested the A/C at the PDI. That's something best to not leave the dealership without it being fixed first.
I doubt you can "add" a thermostat to a basic TT that doesn't come with one for the A/C unit. However, there are RV A/Cs that have a remote control "thermostat" that you can use. Here's one that should work for you that comes with a wall thermostat - it can't tell if it's wired or wireless.
https://www.etrailer.com/RV-Air-Cond...r/ADV94FR.html
Problem is... is it a warranty repair or an upgrade? Generally, they replace like for like with warranty repairs.