Why does my 2000 F-150 believes it is "overheating" and disables the A/C?

My truck is a 2000 Ford F-150 ("The People's Truck" edition - 4.6L V6 w/ no
amenities other than A/C and a tape deck, and an extra long truck bed/wheel
base). After diagnosing A/C problems I discovered that my freon was virtually
empty and that a Schrader valve was leaking. After repair ice-cold A/C was
enjoyed until the A/C halted blowing cold air. All this time without A/C I had
forgotten - the truck often believes it is overheating and shuts that one luxury
down!

The truck does not appear to be ACTUALLY over-heating as the engine bay
isn't any warmer than usual upon it warning of the over-heat - temperate
needle at all the way 'H'ot - even after driving for an hour in that condition. On
cold days it takes much longer, if at all, to reach over-heat; on warm days, it
can be avoided if driving on the highway and getting plenty of air while on hot
days it happens within 5 minutes to 15 minutes depending if driving on
highway or city.

Power-cycling the engine OFF and then ON again "resets" the needle reading
the temperature to at least mid-way between 'C'old and 'H'ot and buys about
another 5 minutes or so before it gets to 'H'ot / overheated.

This has been an issue for some time. Thinking its cause may have been a
missing engine fan shroud (the one in front that will chop your fingers off), I  
replaced the missing shroud. It did nothing for the over-heat other than slightly
delay it.

Any ideas what is causing this? Having my newly repaired A/C shut off after 10
minutes when it is needed the absolute most - a 98+ degree day - is very
irritating.

Thank you all in advance!