In about 30-40 supercharger sessions, only once have I seen a charge drop to 0kW, and then spontaneously restart. I vaguely recall that it was overcast, and there was some lightning in the distance.
This morning, the home wall connector (WC) that I've used ~100 times would not even start. But in that instance, the WC showed a red status light, and a simple pushing of the 'reset' button got it working again.
I've never had any interruption that occurred because of apparent heat or cold.... and your situation seems to have a moderate temperature -- so that would not be to blame.
Since I've not seen anyone report a situation similar to yours (after reading these forums for about 3 years), my guess is you are experiencing
- Intermittent hardware fault in the car;
- Intermittent hardware fault in your Wall Connector (or UMC or whatever);
- an unusual software condition that is triggering stop/starts (perhaps even bad data from a sensor).