The gas valve has a long copper cylinder called the bulb which senses
the air temp. It's probably dead and is not replaceable.
You need a new valve or a new heater.

Dave M.

I just looked up "modulating, bulb-type thermostat" and realized that it
would adjust the size of the flame rather than turn it on or off. Maybe the
adjustment range is too small, and I could adjust the spoiler screw on the
burner to reduce the size of the flame. It's rated at 14,000 BTU/hr normal
output and bakes us unless it is 45deg outdoors.