As promised, I'm slipping into my schedule of doing an hour of work on the car per day, three days per week. With my newly purchased work lamps in hand, I went out and poked around under the hood.
I'm using my Haynes guide as reference for debugging the overheat problem. The first thing I did was check the coolant, which was indeed low. It was topped off to the appropriate level, but was still having the problem. I then checked the serpentine belt, and it is in great condition. So no problems there.
It was at this point that I reached out to a local pal of mine named Brian who was recently revealed to me to be a "Big gear head." I've been shooting emails back and forth with him in an attempt to diagnose the problem and isolate it, so that I don't do more work than is necessary.
I checked inside the oil cap to see if there was any grey residue, which according to Brian would indicate a head gasket leak. Fortunately, it was clean.
I then fired up the beast, and let it run for a few minutes. After about three minutes, the temperature guage rapidly rose to the half way mark, but sad there steadily for the next 7 minutes. The car was just idling, not being driven.
After shutting the engine off, I checked the upper and lower radiator hoses. Both were cold, as was the coolant return hose.
Brian believes, based on this information, that the problem is the thermostat. Fortunately, this seems like an easy enough repair.
Unless I hear differently from Brian within the next few hours, I will pick up a replacement thermostat for the caprice tomorrow.