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Let's assume for a minute that the Power Button is not the culprit of the reboot. Its certainly possible that the button causes reboots during Boot. Several people have discovered, this button can get stuck.
So given that, let examine your Reboot. You may have to try a factory reset to see if that helps. Typically if there are a lot of background apps running, the phone may get warm and reboot.
Speaking of temperature, you may want to use some Battery Temp monitor like TempMonitor. Stock firmware tends to have low tolerance for temperature and may force Reboot.