[Sohcahtoa82]

Yeah, but how much can that capacitor do?

I had a dash cam years ago that had a capacitor, and all it really was for was to make sure the camera could finish a write operation and close the video file gracefully to avoid corrupting the last segment. Cameras with batteries often can support recording even while the car is off without draining the car's battery.

IMO, the solution to the battery-in-a-hot-car problem is to have the battery be an in-line part of the power cable that can be placed in the glove box, outside the direct sunlight, rather than building it into the camera itself.