I've been trying to reproduce this for a while now, and then I had a realization.
I was surprised to hear this, since it's the same basic battery temperature code I've been using in all my aircraft. I couldn't reproduce this with a 50% drained battery, 140°F ambient temperatures, and maximum electrical load in the aircraft. Then I remembered a problem I hadn't seen since my Analog King Air. MSFS erroneously connects the generator output to the propeller speed, instead of the gas generator in free turbine aircraft. Apparently my last minute beta range changes before release dropped the RPM just low enough in beta that the generator doesn't output sufficient power, and the battery is taking all the load.
This problem will go away as a result of my beta range fixes in v1.1, but in the meantime, the fundamental problem is low propeller RPM. If you just keep the power lever at the flight idle detent when you don't need beta for taxiing, the battery will recharge and cool down.
Feel free to pass this along to the Official Forums. We're planning on getting v1.1 out this week, as soon as Boris and Just Flight are back from FSWeekend. Sorry for the delay!