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You're right though that PoGo itself is fairly heavy on resources (I play another game that is seemingly much more involved and it's nowhere near what PoGo pulls) and my phone (HTC 10) will go into thermal throttling (lowers the charge current, clocks down the processors, etc.) when playing PoGo and charging at the same time. Usually when I end up charging mine it'll be in a car and the car holder is a vent clip type, so I just blast it with the a/c and rarely have any issues.
Buy a portable battery. I have this one: [link]