There are 3 water temp sensors and all are in the same relative location. One for dash gauge, one for ECM and one for idiot light. Believe whatever 2 of them are saying. If it hasn't been done for a while it might be a good idea to blow out the radiator. The shop rag test is a good indicator of how much air is passing through the radiator. Start the truck and turn the fan on, then stand in front of it with a cloth rag and put it on the grill. If it hangs on the grill in multiple locations both low and high it's pretty clean. If it falls off it's plugged.
Alarms shouldn't be going off until above 220*