I am not certain that the temperature reported in EXIF is the temperature of processor. It could be sensor temp. The sensor temp would be good to know for noise in long duration shots. The sensor would cool much more quickly as the processor is much deeper in the camera. Just my wild guess.
You could rent both to test with your setup.
Edit: you could also get an external recorder for the GH4. If you have a beefy computer the Blackmagic intensity 4k might work for a studio setup.
I wonder how the camera will handle 6k. As far as I know HDMI 2.0a does not support 6k, so an external 6k HDMI recorder might not be possible yet. I think that would leave a proprietary external recorder or internal 6k recording.