Click on the picture for more info.

The outer two lugs (silver) are the thermostat contacts. They should open at 135 degrees F and re-close at 120 degrees F. At least if I read the label correctly. This will be on a high heat setting re: internal heater should be off.
The inner two (copper) are the thermostat's internal heater. They usually run 5,000 to 10,000 ohms

Not sure what the problem is as it is normal for a heater to cycle.
More info on what is happening might be helpful.

You could check the exhaust temperature to see if the thermostat is operating correctly