I don't think the "quality" of the thermostat is an issue here. A thermostat is realy nothing more than an On/Off switch.
Does the ON?OFF switch have a thermostat position? In other words is the switch set up as ON/OFF/THERMO? By the way the wiring shows it "should" be.
The Red wire brings power to the switch and the switch position shunts power either thru the Black one wich turns the gas valve on all the time or thru the white one which allows the thermostat to control the gas valve. It sounds like the power is always going to the black wire. How is thw wiring set up at the switch? Can you show a picture of that?
Does the ON?OFF switch have a thermostat position? In other words is the switch set up as ON/OFF/THERMO? By the way the wiring shows it "should" be.
The Red wire brings power to the switch and the switch position shunts power either thru the Black one wich turns the gas valve on all the time or thru the white one which allows the thermostat to control the gas valve. It sounds like the power is always going to the black wire. How is thw wiring set up at the switch? Can you show a picture of that?