I have a furnace that is about 20 years old. When the furnace is first turned on everything works perfectly... it lights like it supposed to and runs for around 3-5 minutes then the burner shuts off and immediately tries to relight itself. It relights and the burner only runs for around 3 seconds before it goes out again. It tries relighting another two times and then just quits. I have cleaned and tested the flame sensor, and I have tested the pressure switch. If I like it cool completely back down and start the whole process over again it will run for 3-5 minutes again before it goes out and then will only relight for a couple of seconds. Does this sound like a problem with the fan limit switch? Please help me.