Re: What about heat?
I think it's just a question of trade-off of charging speed vs capacity. Say they can charge a current battery of approx 2000 mAh in 30 seconds instead of 1 hours (X 120 speedup). They don't necessarily need to get 120X efficiency improvement. Say you tweak the charging capacity so it can charge in 2 minutes, or 5 minutes instead of 30 sec, that's still a huge boost in charging time and gives more time to dissipate heat.
Secondly, if it were possible to charge a battery to full in 2-5 minutes or half a charge in 1-2 min, you don't need such a large battery. 2000+ mAh have evolved to accommodate full-day heavy usage since phone needs to be charged 'overnight'. But if you can top-up quickly (and also because nowadays usb-based chargers are standard, pretty much everywhere there's a socket), many phones won't need such a huge battery, 1000mAh will do.
Thirdly, many phones now have a super-low power use setting so some phones might work with an even smaller-capacity battery.
Wouldn't work for all phones especially high-end. But for phones that are only used as smartphones a minority of the time and in an urban environment where charging points are everywhere (which let's face it, covers probably a majority of smartphone users) , they don't need that much of a charging efficiency improvement.