After unsuccessfully trying to change the blown light bulb I discovered that the plastic light socket had gotten so hot that it melted and permanently fused with the blown bulb. After my new socket arrived in the mail I just popped the temp control assembly out with a screw driver and removed the old socket and placed the new one in. Whole operation to 5 minutes.
I removed the cover, used a multimeter to test the compressor circuit, and found the compressor start relay to be defective. Ordered a new one and installed it when it arrived.
Removed the cowling with a square drive screw driver, removed the spring clip from the cover of the compressor controls with a screw driver, pulled off the old compressor start relay and replaced it with the new part. Since other problems could have caused the compressor to short cycle this was a "replace the part and hope it would work" since that would be the most common reason and it was not a very expensive part.