The only options you have:
1. DFU restore by downloading a fresh 8.0.2 ipsw file (set the phone as new)
2. Do a hard reset (set the phone as new)
3. Wait for 8.1 software update which should be available to us within a week.
Happened to me three times. iOS 8.0.2 5s
Any thoughts?
This has happened a few times to me on my 6 Plus with 8.0.2. Goes to the white screen with black Apple logo for a few seconds, then back to normal, not a complete reboot. Probably just a bug.
Off subject just a bit but have you noticed the background on the reset screen matches the bezel color? When I get the respring I have a black background with a white logo on my space gray phone.
Anyhow. A reboot here and there has been needed manually. I would take an auto reboot. I could save some time/effort. I'm joking a little and hope too 8.1 cures a few things. Mostly happy, just ready for the next update.