Does it turn on and stay on or is it a momentary "on" and automatically go off with a minute?
It could be a couple of things:
Bluetooth could be on and that will cause a BT enabled device to wakeup when another BT device comes into range.
It could a remant (preference file) from a program that has a trigger to turn the device on to check something via BT. Lets say you have a program set to automatically check for updates via your cell phone "once a day" well the program might be triggered at a specific time - it will wake up the device but you may not see any activity.
Also, T5's had an issue early on (if you didn't apply the update) that would cause the device to come on at 3:30AM for no apparent reason. This was mostly triggered by a Birthday or Anniversary reminder for a birthday that was in the first 8 days of the year (January). The update was supposed to have addressed this.
