I've been doing some extensive digging for a 2a Qi system myself. The highest available system is unfortunately 1a. BUT... In order to get the 1a, not only does the charger (transmitter) need to be rated for at least 1.5 - 2.0a output because of poor efficiency, but your receiver in your phone needs to be rated at a 1a output. This is why you see several people who are only charging at 600-700ma. For my Note 3, I have found a 600ma, 700ma, & finally a 1a receiver coil. The Samsung charging backplate is actually only rated at 600ma. Just make sure you look before you buy. I bought an Itian A6 charger combo and it only has a 600 also, but the transmitter I believe 1.5a. I'll just have to pick up another coil once my charger arrives. Damn China Post takes forever.
Anyway, hope this helps answer your questions. Wireless Consortium approved a medium voltage guideline and I just read that they have come out with a Qi system that is 97% efficient. Our power demands just need technology to catch up.
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The heat is due to the inefficiencies, most Qi chargers lose 25% of the transmitted energy, which ends up being the source of heat. The newer 97% efficient chips will be much cooler. Also a good receiver coil is thermally protected and will shut down the charge at a threshold temp. The quality of the receiver coil is the most important part of Qi. But don't forget, charging any battery rapidly will cause heat as well. There was a news story about 2 months ago of a kid who slept with her phone under her pillow and caught fire from improper ventilation. If your phone is heating up that hot, you may want to remove any case it's in. Charging up with Qi and a metal backplate isn't exactly the smartest thing to do either.