[ndutton]

I think you're headed down the right path for the most part. Coolant loss is the most likely cause of your elevated temperature and there are very few places the coolant can go:

1. Leak out and end up in the bilge - not in your case
2. An internal block breach into the crankcase - also not in your case
3. Manifold breach sending the errant coolant out the wet exhaust (who would even notice?)

Therefore I suggest a manifold pressure test is in order.

For the shut down I would approach it as separate from the elevated temperature. Testing is best performed at the time of shutdown and the first determination is spark or fuel. Once that is known the real troubleshooting can begin.