Have you looked into System Preferences>energy saver>schedule? Maybe it's set up to start itself, or resetting the PMU might help.
The PMU (Power Management Unit) is a microcontroller chip that controls all power functions for the computer. The PMU is a computer within a computer. It has memory, software, firmware, I/O, two crystals, and a CPU. Its functions is to:
-Tell the computer to turn on, turn off, sleep, wake, idle, etc.
-Manage system resets from various commands.
-Maintain parameter RAM (PRAM).
-Manage the real-time clock.
1. Disconnect the power cord and check the battery in the battery holder (BT1). The battery should read 3.3 V to 3.7 V. If the battery is bad, replace the battery, wait ten seconds, and then reset the PMU (refer to the next step). If the battery is good, go to the next step.
2. Press the PMU reset switch (S1) once on the logic board. Do not press the PMU reset switch a second time because it could stop the PMU chip from responding.
3. Wait ten seconds before connecting the power cord and turning the computer on. If the computer does not turn on, there is something else wrong with the computer.
This entire procedure resets the computer's PRAM. Be sure to reset the computer's time, date, and other system parameter settings.
Good luck $BoomBoom$ ;D