Not really a problem anymore (my E12 is perfect really), only a matter of curiosity:
Do you use your E12 as a desktop amp as well, like do you leave it plugged in and turned on for days?
I used a 2.4A USB wall charger, and it didn't get hot when charging while turned off. It's weird. But maybe because it was already partially charged? I'll try again when it's drained.
At full charge, when turned off, the E12 shows a stable charge light. When turned on, the charge light is stable for an hour or so, then it starts to blink slowly. Then it doesn't stop blinking and gets a bit warm after 10 or so hours, definitely not as hot as before when used right after the battery was almost drained. It's really mildly warm, like benchwarmed-bench warm, my Galaxy Nexus gets scorching hot when using GPS in comparison. I'm just trying to determine why when using it after a full charge, it goes on to a slow charge while plugged in. I thought the battery isn't used when running on power?
I'll test again to make sure if the E12 gets a bit warm when running on battery. That means it's normal operation and not related to charging.