The thing that fixed my phone from auto rebooting by itself randomly is to go into your Play Store option and set Auto Update Apps to 'Update over Wifi only'. I had set it to never update. I can't get into why it happens since I don't know where to check logs but this does work for me. (Menu>Settings>Auto-update apps)
My story: Yesterday my phone reboots by itself every few minutes without even touching it for no reason at all. Phone had about 75% juice. I remember doing the unlock and had no problem with it for the whole day. I was at jury duty, boored and I was messing with options to restrict background data and changed the Play Store update options to Never Auto Update Apps since I switched to Tmobile and I don't have an unlimited data anymore. Afterwards the phone started rebooting by itself at various times during the day. I didn't notice until later on the night where it rebooted itself every few minutes. So I tried out various fixes which didn't work and set Airplane mode stopped the rebooting but wasnt a fix. After awhile I tried to retrace all the stuff I did on my phone during the day and strangely setting the option back to Auto Update Apps to Wifi Only fixed it. After doing that the phone stopped rebooting by itself and I was able to use it all day today.
So basically, see if setting the auto update to wifi only if you had it off will fix this.
Also I realize there are many different fixes other users have reported like the Power Cycling, Airplane mode or Clearing Dalvik and Cache(Which didn't work for me), or even reflashing/reset to factory (I avoided this). None of those worked for me. If those didn't work for you, try this as another option.
Mods: Please move this to Sprint Samsung S4 section. I have no idea why I'm in this section. I'm sure this applies to every S4 though.