My Intertherm furnace stops heating, but continues to blow air. So I wake up and turn it off. I open it and push this tiny red "button" (which is surrounded by wires, looks like the end of a very tiny pencil, and gives a soft click when poked) and then turn it back on. This kicks the heat on for a few minutes and then the blower blows lovely warm air for a while.

Then, I go back to sleep (or whatever I'm doing) and after a few minutes, the heat goes off. The blower stays on and will continue to blow out c-c-cold air. When I can't stand it anymore I turn it off. I either repeat the process or leave it off and burrow. When I'm getting ready in the morning, I turn on the heat so I can shower, then quickly get dressed and turn the furnace off--or it will run cold all day.

BTW--the tiny red thingy doesn't make a click when the furnace is actually running correctly--only when it is not right.

That is an auxiliary limit... if it is near the burners you either have a bad auxiliary limit or you have a bigger problem with flame roll out. My suggestion to you is to call a qualified technician in to troubleshoot the problem.