We've been using an old hat similar to the video, but we also put a gel icepack in it and a cooling towel over the camera. A bit tedious to setup in the beginning but it's lasted through triple digit heat with that combo.
So I streamed two games today with the mevo. 8am-11:30, no covers. No heat issue and did not need to use an external battery.
As for my phone, that I did use an external battery and an ice pack as my internet streaming point.
I must admit, the mevo is very plug and play with game changer. I also like the video recorded to card is a single file and not broken apart like GoPro