Might be an old thread, but I'm putting this up for other to see in case it helps.
A 2001 truck could be either Single OverHead Cam (SOHC) or Dual OverHead Cam (DOHC) because the DOHC engine was introduced mid-model-year.
I'm going to take a chance and assume yours is a DOHC based on what you said.
There are 2 coolant temperature sensors on your engine:
There is one that reports temperature data to the gage on your dash - it is built into the thermostat that is mounted on the engine block behind your water pump on the driver side of the engine. Unfortunately the thermostat is an unusual design and as a result is (for a thermostat) extremely expensive, $140+.
The other one is mounted on the waterneck at the back of the engine on the passenger side. If you follow your upper radiator hose back to the metal pipe (waterneck) and follow that to the spot behind the cylinder head where it bolts to the head you'll find this ECT sensor. The price for this one isn't to bad because its a normal design, should be around $30.
There is some debate about which reports what to the computer.
1 - I replaced the ECT sensor on the waterneck and it did not fix my problem (no temp reported to gage), so I can only speculate it reports its data to the PCM.
2 - I bit the bullet and bought that expensive thermostat - that fixed the no temp problem. I've also read that after the first couple of years that engine was used in our truck the super-expensive T-stat got replaced with a less expensive one (I think I read it was something like 2005+) that works just as well and fits the same pigtail.
If you want to see some pictures, check out this thread: (pictures are down at the bottom of the thread)
Coolant sensor ?