I have been having the same issue and here is a timeline of what I have tried so far (with no luck):
Updated to 8.3 two weeks ago (no issues at time)
April 30th ATT sent a carrier update
May 1st device started doing the restart only when plugged in to charge (docking unit, Apple charger, and USB from computer - same behavior)
Tried disabling carrier, Bluetooth, and wireless with restarts in between with no changes
Tried reset of device (not a downgrade of IOS) with no change in behavior
No applications were installed between 8.3 installation and now, but multiple applications have had updates. Battery indicator seems to be working correctly (seen in other posts where the battery does not show decrease in power consumption - not experiencing)
I am guessing the issue I am having is something involving the carrier update since that seems to have been the trigger for the problem to start, however, I am seeing in the Apple forums where multiple people with different devices (4s, 5, & 6) having similar issues