[JRTJH]

I'd make a guess that it's probably the thermostat, but since we're "in the mode" of making alternative suggestions like outside shower faucet valve settings and winterization valve position, there's a possibility that the one way valve at the water heater outlet may be stuck.

The winterization system is composed of a 3-way valve at the bottom (water heater inlet) and a one way (backflow preventer) valve at the outlet at the top of the water heater. There is a "vertical bypass tube" that connects the 3-way valve to the output of the one way valve, isolating the water heater during "bypass"..... That one way valve at the top of the water heater must open freely to allow hot water out of the water heater while closing freely to prevent backflow into the water heater when winterized. A common problem with water heater "less than hot water output" is calcification of that one way valve. If it gets "sticky" it won't open fully it can cause the water at all the faucets to be insufficiently hot. So if changing the thermostat doesn't fix the problem, I'd look at the back of the water heater, on the top outlet. You'll find a PEX tube connected to a "brass and plastic" fitting. That's the one way valve.