I have similar unexplained incidents.
I will next time it happens, check if the fan is running. The fan is supposed to run with A/C on to cool the evaporator. I believe if the fan does not work, the AC will register high pressure and switch off.
That, however does not make a lot of sense, if it happens while the car is moving, as the ram air effect should be enough. But I would check in any case.
Another possibility is a temperature sensor malfunctioning. I have seen that happen on my other Rovers for engine temperature and outside temperature, only for them to recover at next switch off and be fine for long periods.
It is really irritating that there seems to be no good pattern to this, except getting loads and loads of stinking hot air through the fascia vents.