This is basically a "me too" response to add to the thread. Installed the OS 10 update through iTunes on Tuesday. Upgraded my iPhone 5s. Immediately noticed my phone get VERY HOT when plugged in. Stays HOT when unplugged and in use. Battery drains like crazy, goes from 100% to 90% in 10 minutes. In an hour I'm nearly fully drained, sitting between 5-10% with moderate usage -- reading email, texting, reading news, changing settings, contacts, calendar, surfing a couple Web pages etc. (You know, the things you do every day with your phone!)
The phone used to go for hours on a single charge, 100% unplugging in the morning at 7am to about 50% at 5pm. Mostly light usage during the day, but lost of checking emails, texts, etc.
After I installed 10 and noticed the heat and batter drain, I immediately turned off automatic updates of apps. Turned off all background app refresh. Turned off 95% of app notifications. Turned down the brightness to 25%, turned off auto brightness. Turned off push notification in email. No change in battery drain.
I have since tried recharging the battery while it was off and using the on/off button + home button reset. No improvement there. Have tried removing all widgets, no improvement in battery drain either.
I am not using moving wallpapers. Siri is turned off. All iCloud backup features turned off. Turned off share my location. Turned off 90% of location services. Turned off searching for WiFi networks. I have basically turned off most features I can think of that might affect background battery power.
I turned off nearly all new features and many typical smartphone features that I used to have on all the time, and still the battery drains like running water. And the phone gets VERY hot. This never happened before 10.
I am thinking about reverting to my backup in iTunes.
What a pain this has been.