Autopilots, Crosswinds and Air Masses

Is it valid to say that if you fly in a strong "crosswind" at altitude and there's a constant change in windspeed/direction that the autopilot/roll servo will constantly have to correct the flightpath?

Yes, correct.

Will this make the motor in the roll servo get hot eventually and could that be the reason for the A/P to disconnect if the the servo is not perfect?

I doubt that the servos have temperature sensors, but the electronics inside your AP control box will be protected against over-current and maybe overtemperature which might cause the disengagement. On the other hand, the task you describe should be well inside the design limits of any autopilot and not cause disengagement, so I suspect a fault somewhere!

What you are describing would be turbulence. Have you flown through extensive turbulence where the autopilot dropped out regularly because it was hitting its limits? Outside of turbulence, there is hardly anything that would put a lot of stress on servos.

Is it valid to say that if you fly in a strong "crosswind" at altitude and there's a constant change in windspeed/direction that the autopilot/roll servo will constantly have to correct the flightpath?

Technically yes but only if you are flying a Rate 10 turn in the middle of a tornado

The heading adjustment for any normal wind direction change enroute is utterly negligible and is orders of magnitude below (in servo motor activity) normal roll activity keeping the wings level.

I doubt that the servos have temperature sensors

I think these are just old dumb servos, like the early King KS ones i.e. motor+gearbox, clutch, and probably no electronics. The AP computer certainly gets no feedback on anything from the servo (the wiring shows no such connections).