Well, the new water pump is in. No improvement. The temp on the heads is consistent and good. Both the temp sender and the CTS were replaced, and the temp sensor pigtail was replaced. The gauge (which is calibrated) was reading in the red, but the coolant was only warm at the CTS.
The only thing I can figure is that there is a short somewhere. Any idea where? The issue seems to be worse while the car is stopped--even in park, so not the brake pedal.