Lighting, Light Fixtures, Ceiling and Exhaust Fans - Recessed Light Goes on and Off

I have a recessed light (R-30) that had been working properly for 15 years. All of a sudden the light would cycle on and off. The light bulb had been installed for about a year. The fixture is one of two fixtures in this circuit and does not have insulation in or around it. I have installed another 65W bulb, a 40W bulb and an energy saver florescent bulb and it still cycles on and off. My assumption is that there is a thermal switch of some type but I do not see anything inside the looks like a thermal switch inside the can. This fixture non-adjustable. Can the switch be in or around the socket? The installation (in a mirror) makes it difficult to remove. Any suggestions?

Yes, there's a thermal switch in there. Sounds like it may have gone bad. Replacing the whole can may be easier and no more expensive than replacing the thermal switch. You can remove the can from below without damaging any finished material, even though you currently don't think that is possible, and probably still won't think it's possible for the first ten minutes you try to figure out how.

This worked fine. Thanks.