rethreading thermostat holes from 5/16 to 3/8 ?

To answer your question...i have done that and it worked fine.Are there other options...absolutely.
Thanks, I just checked a Drill Tap chart, 5/16" is the correct drill size for a 3/8"-NC thread. Did a test with a 5/16 nut, you can tap it to 3/8-NC no problem.