Empire model gwt-25-3. Pilot stays lit, raise thermostat and furnace comes on. When temperature reached furnace and pilot turn off.

It could be anything from a safety switch to a thermocouple, but what you need is a qualified tech to troubleshoot and test your system. Who installed this furnace? How long have you had it? Do you have and know how to use an ohmmeter?

I can direct you to an owners manual to guide you but a reliable tech is what you need for HANDS on diagnosis.

https://www.manualslib.com/manual/81...-Gwt-25-3.html

Parts are to expensive to just change and not get to the problem. Do you have a manual and followed the routine cleaning procedures?