I've had this HTC One M8 Windows Phone for just about exactly 2 years now (coincidentally exactly when my contract expired.) I've always had problems with the charge plummeting from 40% to 5-6% in an hour or less and causing my phone to turn off without me noticing. However, just now i was distracted by it turning off after crashing to 5% from 76% in 1 hour (from 100% in 3 hours.) Even more alarming is the fact that, even with NOTHING running AND with it on standby (screen locked,) it was still very hot. It felt literally almost as hot as a winter hand warmer pouch (if activated in a 77 degree house.) I plugged it in, and guess what? The temperature dropped to normal! Since the below pictured 10% measurement (actually 5%,) it's been about 50 minutes and it still hasn't recovered any charge past 15%.
Please respond with a reliable solution. I am a Pilot, and this is my Only mobile phone, so it has to be fixed ASAP.
Steps to cause the issue: None, the screen was locked and no apps were loaded in the background.
Not likely to be battery defect because it's charging now, and not only is it not hotter than it was, but its actually much cooler than when the issue happened. I suspect it was a Verizon software trigger since my contract expired 2 days ago to try to get me to renew for 2 more with a new phone.
The charging itself is irrelevant, it charges fine up to 100%. The issue is the rapid DIScharging that occurs once every 3 days or so, mostly in the evening so far. The charging issue I mentioned (as clarified below) is a result of the phone's discharge rate being strong enough to fight (and significantly inhibit) the charge rate. It's like the electricity from the charger is flowing into my phone, and being immediately purged in the form of heat (and a LOT of it.) My phone has activated a hairdryer mode with no cooling fan. 
The HTC One M8 discharges from 100% to <5% in less than 4 hours. while in standby with no apps open. Since my previous post, it's happened a number of times and below are a few more examples of it discharging. As you can see below, it charges quickly, but in the first picture, you can see it discharging at a similar rate to the charging. Also, in the bottom picture, you can see it the discharge fighting the charge rate as it slows down the charging by half of its normal value for a time. As you can imagine, the phone gets uncomfortably hot when this happens, leading me a couple other times to turn the phone off to let it cool down.
