I have a very old under the floor type of gas heater in my house. It uses an ITT thermostat and I believe it is a millivolt system as it works even when we lose electricity. Lately the range between when the heater turns on and off seems to have increased causing it to be either a little chilly or a little warm but never quite right. The range can be up to ten degrees. Is there an adjustment somewhere to fix this? Which component might be at fault here? The thermostat, the millivolt generator, or the gas valve? Thanks.

Likely a worn out thermostat. Amazingly, there are some modern setback 'stats available. Why would I mention them? Because they have a very tight control range. On a goo one it is 1 degree =/-

I would say it is the tstat if it was the genarator the piloit would not stay lit