That is a very basic millivolt system that can be easily troubleshot using a VOM and manometer.
So you're asking whether it needs a new thermostat. It COULD be. The proper use of a VOM/manometer would answer that question. However, other possibilities could be a loose wire connection, a bad wire crimp, a corroded wire connection, a faulty gas valve or poor gas flow to the burners. Heck, even a broken Unitrol knob could be the problem (not unusual on RobertShaw gas valves when the knob becomes difficult to turn).
Since I'll assume you don't a VOM, a manometer or basic skills/knowledge to determine how the electrical and gas parts work, I'll simply suggest you go in there to check all electrical connections, then go behind the fryer to check that the gas is fully turned on and properly connected. If that doesn't find ‘n fix your problem, then you'll need to call a service company.
If I am wrong about your skills/knowledge, then here's a manual which includes an electrical schematic and some specific operational parameters for you to test.