Is the radiant system an electric radiant or hydronic (water in pipes) system? What's the model of the thermostat?

Can you post a picture of it if you don't have the model number?

CeilHeat Inc. is (was?) an early electric-radiant company "back in the day" ('60s? '70s?) and it's most likely an entirely line-voltage system. I dont' know if there was any sophistication built into the thermostats (PID & anticipating control algorithms controlling duty cycle etc seem like a much later sort of feature.) Any decent electrician should be able to pull the thermostats and give you an opinion, could be you just painted some mechanical aspect into the "contacts closed" position, but don't count on it. You may be able to swap in a sufficiently-rated line voltage thermostat for electric baseboards, or repair the beast in hand.

If you know which breakers/fuses run the system, pull the thermostat- it may have current & voltage specs on it. Anything you replace it with needs to meet or exceed those numbers.

It's a 220 electric. I had my son pull the thermostat and there is a red and black wire going to it. No picture right now but if it will help I can try to get one. The info that is legible on the thermostat is CHT-5 22amp 125/250 VAC. The control is a simple thumb wheel with the numbers 1-5 on it. On the 2 that aren't working one has a lot of rust and the other had something wedged inside the housing.

Thanks for the feedback.  The system probably went in during the 60s.  I did have the voltage checked and its 220.  I may try the local supply house to try and get a couple of repalcement thermostats.

Thanks to Dana's infinite knowledge of 'back-in-the-day' equipment, look to Aube Thermostats. They have many different types of line voltage controls (120 or 240v) you can update your controls to.

These should be easily replaced with a thermostat for radiant electric that has the same knob style configuration with the temp # on them.

Thanks Dave