After resetting/restoring my phone, the battery drain/overheating issue has gone away. All is good again.
Also having the issue with mine. The phone is literally a month old. I have all latest updates for Skype even though I never use it. I have the Dot View case. Battery monitor says something is draining 7.7% of battery every hour. Yet, no programs are using obscene amounts of battery. It hit 35% when at work from 8:30 AM to 2 PM. So that doesn't exactly add up. For the past few weeks, at this point in the day, it is supposed to be no less than 75%. The largest battery usage is Nokia Here maps, but that's same as it was the past few weeks. The heating issue just started this past weekend. I am very habitual when using this phone and only have a few apps.
I know foursquare had a huge update recently, so I uninstalled that and hopefully it helps.
PS I have no Developer Preview on mine, regular 8.1.
I have been monkeying with this for some time myself. I don't use Skype, but like a lot of folks suspected the dot view case, I continued to have the problem even with the case removed and software disabled. I had reset my phone twice as well leaving only the default apps and it still had a problem.
What I noticed was that I never had the problem at my office while connected to the wireless. It seemed to always get hot as I was out and about, inconsistently for sure. Like everyone else if I went into airplane mode the phone would cool. Sometimes I could even restart the phone and it would continue to get hot after it booted. I travel quite a bit and noticed this was common in airports and at a diner a few weeks ago it was sitting on the table and got very hot, rebooting didn't resolve it, and I had to shut it off completely lest the battery drain completely away.
What I ended up doing was disabling the Wi-Fi Sense stuff in the WiFi Settings so that the phone would stop trying to log into wireless networks automatically. So far it has been over a week and the heat up problem has not returned. I hope my suspicion that this application in it's zeal to connect with certain types of WiFi networks is the problem.
Ok, so, I think I MAY have fixed my issue. I'm cautiously optimistic. After a day it hasn't happened, and trust me for this phone that's a good sign.
How many here use Baconit or Readit? Those two apps were my problem, I think. I would notice that it seemed to start after I got done using either app for 10-15 mins not on wifi. So I reinstalled, and I refuse to open either app if I'm not on wifi. I just use IE for it. Today, it has worked well. When I went out, I purposefully used a lot of data just to test, but didn't open Baconit. And it was cool as a cucumber.
I know both apps are battery hogs, but it shouldn't be like this. There is a problem with this device that needs resolved, but I think I may have found a temporary fix for now, at least for me.
And no, Battery Saver wasn't reporting it using any abnormal battery amount.