I have a Mueller Climatrol Furnace VR8200A 2132 model that has been in the house for over 20 years. It recently started blowing cool air. Repairmen came and oiled the motor and that did not help so they replaced the motor and the fan switch. Now the furnace tuns for one minute and turns off for 2 minutes and then cycles. They then came and replaced my thermostat and it is still doing the same thing. Now they are suggesting I start looking for a new furnace. I have read that a dirty burner could cause this, or a bad flame sensor could be bad. I don't know where to look.
Any suggestions?

It sounds like you had a couple of morons who did not know how to use a meter. You need to find out why it's not working with a meter. You do not just change one part after another and think you may hit the right one. It doesn't work that way. Oiling the motor had nothing to do with the thermostat or any reason that would necessitate getting a new furnace. In a new furnace you could have the same problem. Look at these and understand them: https://dl.dropbox.com/u/8010163/AC%...20Diagrams.zip
https://dl.dropbox.com/u/8010163/How...e%20Manual.pdf