Are you doing something when it restarts, or is the phone just sitting there on standby when this happens?
The so-called "white screen of death" on iOS 7 was pretty much the same thing -- random restarts occurring for no apparent reason. It happened to me once every few days until iOS 7.0.4 came out. But, that flaw was well-known and Apple acknowledged that a software bug caused it.
I haven't seen this as a common complaint about iOS 8.0, so you might want to start with a restore to factory settings, and then reinstall iOS (although you might want to wait until the botched iOS 8.0.1 update gets fixed first). And then restore your phone from a backup (assuming that you've already backed up your phone). Otherwise, you can always make an appointment at the Apple Store. This is the kind of thing you want to isolate as quickly as possible, because defective hardware could also cause it.