In the end, the best supply I could find could only provide 6A (at 13.8V). I set that up and let it run for about 90 minutes while I poked around for better options (found a few duds, but nothing that could provide the right combination of current and voltage). FWIW, I measured the field in the bore to be about 1000G (at 6A).
To do a full current test, we need a supply that can deliver 10A at ~25V (the magnet has R=2.3 Ohms).
The temperature was measured at multiple locations on each coil and was found to be quite uniform during any given sample. One coil systematically read 1--2 degrees cooler than the other coil.
The magnet was left on the 'BigBite Computer Table' in the Hall.
These data are for the magnet at a constant 6A:
Time Temp [min] [C] 0 23.9 14 30.6 21 33.9 43 39.4 72 45.6 92 48.3