It no longer has a battery. So there's no reason to be off while plugged unless you shut it down while it's plugged.
Go to BIOS and under power management you will see an option "Wake on AC" or "Power on AC," mentioned. Just disable or unclick this option and you are done. BIOS settings would be different in different brands, but the steps are same,. You just need to disable or unclick the box next to this, so that the laptop does not power on when a adapter/charger is plugged in. It should be okay to leave it on with the screen off.
Laptops have things like Hibernate, and Sleep modes that control the on time. If you like to keep your laptop powered on for days at a time, you will have to change the hibernate and sleep settings. Heat is a bad thing for laptop computers.