I'm using external battery, It's a lifepo4 battery.
I haven't thought about the battery performance. It could be overheat protection from the battery that cut off power to the dashcam.
For reflective windshield, Is cover only the windshield effective?
I'd put the battery in a small cooler or insulated lunch box and run a cable in to charge and out to power the camera.
Your typical reflective windshield sun shade that people put up when parked do reduce the temperature in the vehicle as a whole substantially. The trick is what do they do to the temp between the shade and the glass, is it about the same or is it higher.
You could put up something like
this and cut a hole in it for the camera so most of the electronics are on the cool side of the shade. This has potential to affect what the front and rear cameras can see. Depending on how your vehicle is orientated relative to the sun, shading or tinting other windows may do more good.
Some window tints that can be applied directly to the glass may help keep the vehicle cooler (probably most, I say some because some are going to be more effective)