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What does the car and EVSE show when this shutoff occurs?
The car may be shutting off due to no ground wire detected and other handshaking between the EVSE signaling it to stop.
Also, what is your charge limit set to in the car? You should set it lower on a shared breaker. Since this is shared with other appliances I assume it is 120V Level 1 and not 240V Level 2. The car allows setting a charge current limit for Level 1 only. This can be set via iDrive or the MyBMW App.
Charging when the batteries are warm isn't a concern as the car will cool the batteries as needed to keep them in a safe range when charging...
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