MR1100 shutting down and battery overheating

My Nighthawk M1 Mobile Router is consistently overheating while in use and plugged in, even in cool (~50F) ambient temperature. This results in slow/stopped charging, and frequent random disconnects. I have already sent back one unit for these problems, and the new one is showing the same behavior. I see some references in this forum to updating firmware to solve this issue, but my firmware is up-to-date (12.06.11.00).

Can anyone suggest any solutions that aren't "don't use while charging the battery"? This router came so highly recommended, I find it hard to believe that there's no solution for such a major and basic flaw.