One recessed (in the ceiling) indoor floodlight (85 watts) on a single switch goes on and off in sporadic intervals. Replacing the bulb does not remedy the situation. The connections appear to be in order. Any suggestions?

The thermal protector is shutting off and on. I would have to assume that the fixture is rated to handle this lamp, so the thermal protector must be weak and defective.

See if you can see the thermal unit mounted up inside the fixture, find the brand and model number, and go to a lighting distributor to see if a replacement can be purchased. You may find it cheaper and easier to just buy a whole new housing and replace it rather than trying to deal with just the thermal unit.