Yes, of course there are things Blizzard could do to fix it.
For one thing, they could limit the frame rate.
Playing on PC, I can clearly see that the game runs the GPU as hard and fast as it will go, rendering as many frames per second as it can. It renders at hundreds of FPS on my PC. Constantly. Even when idling at a menu screen. Obviously, this is incredibly wasteful of power, and the charge cycles needed to support it are needlessly destructive to any battery-powered system, like a phone.
Blizzard, isn’t this game built on the Unity engine? Unity supports FPS limits already. Won’t you please make use of that feature?
Also reported here.