Check if an automatic power up was defined in bios setup. Thats usually in
Bios setup's power management menu (should be disabled or set to 00:00).
If none was set, your case is possibly suffering from a faulty or
misconnected power button. Usually caused by a capacitive load which
eventually triggers. Download mobo manual and disconnect the power_on jumper
overnight to test.
Also, depending on mobo involved, you might be suffering from a Wake-on-Lan
or Wake-on-Modem feature that misbehaves. These can be disabled through bios
setup and the WOL connector removed between NIC and motherboard, if any.