Be careful on the wiring issue, I would bring up the hidden OBC menu and watch the coolant temp.
I have only 1 time had a Coolant Temp code after I had changed the tstat. I actually had the OBC displaying the temp and was watching it the entire time I was driving. I had a stretch of road that was about 50 MPH for about 3-5 miles. I came to a traffic light, stopped for a few minutes, made a left turn when the light changed and on pops the CEL!
Turns out I had temp and cat converter codes, I called BS on this, reset the codes, no problem since. I think that at times under light load the O2 sensors may cool off and start to get lazy and possibly trigger these codes.
My O2 sensors are only about 6 months old and I feels that maybe the light load, long cruise with cooler outside air temps can cause this??