I have the same exact problem with my iPhone 5s. Since upgrading from iOS 7.1.2 to iOS 8 and now 8.0.2, my battery drains very fast and the phone heats up more than ever.
Like you, I close all my apps on a regular basis, but the problem persists. Here are some of the steps I tried that did not solve the problem (not listed in any particular order):
- turned off Location Services for apps that don't need my location (which is most of them)
- turned off Background App Refresh for apps that don't need it (which is most of them)
- performed several hard reboots and regular power off/restarts
- turned off all System Services except Find My iPhone
- turned offSend Last Locationfor Find My iPhone
- turned off Share My Location
- reduced the screen brightness
- set Auto-lock to 1 minute
- changed my email from Push to Fetch every 30 minutes
- synced with the latest version of iTunes on my laptop
After all those steps (and probably a few I can't remember), my battery is still draining way too fast and the phone is heating up too much. It is unacceptable. I need Apple to release a fix for this ASAP.