I know my 2000 3.0 V6 temperature gauge is faulty. When cold, the needle is at it's low mark. When the engine warms up, it rises to the center of the gauge.

I week ago during an e-fan install, I allowed the engine to warm up, and as I was testing the temp probe for the e-fan, the coolant began to get hot, as I could hear it gurgle in the radiator. I shut the engine off quickly, and waited several minutes for it to cool. During this time, the temp gauge never got past the middle of the gauge, indicating the coolant was fine.

So to test the guage/sender, I should be able to remove the "one wire" connector from the temp SENDER (I know the PCM uses a two wire SENSOR), ground this wire, turn the ignition key to on, and the gauge should peg to the top. Is this correct? If the grounded wire does not peg the gauge, then either the gauge itself or the wiring is bad. If the gauge pegs, I can suspect the sender?

The engine has 2014K, and the sender appears to be the original one.

A few weeks ago I replaced the "slosh module" in the cluster to fix the fuel guage not reading correctly (filling the tank only gave ve a 3/4 indication its guage). The slosh module fixed that, but now I'd like to address the temp guage. I know these are not 100% accurate, but the guage should have indicated to me that the coolant was hotter than the "normal" half way reading it gave me during my efan temp probe calibration.

 

Yes, that testing method is correct.

If you had air in the system it can cause the gauge reading to be off, sender reads liquid temp so air bubble at the sender will cause a lower reading until metal around sensor heats up.

The temp sender, like the oil switch sender, uses the engine as the Ground, so it only needs 1 wire, people often use sealing tape on a sender's threads, do not do that.................it will cause incorrect gauge readings.
Leave the lower threads bare for a good ground to engine.

 

Removed the sender, grounded the wire, and presto, the cluster gauge pegged high. Replaced the sender (have the new one handy to pop into the hole to reduce the amount of coolant loss).