I bought a 750W (nominal) inverter a couple months back. I found quickly that my laptop would not run with the truck off when powered through the cigarette lighter adapter. Fortunately, my truck had been wired by the PO for a large audio amplifier to the passengers side rear access door in the back. further, both the neg and pos wired had ring terminals so my inverter attached readily. So I used a coupld cable straps to secure the inverter to the rear seat rail. This lets it get plenty of air to stay cool and allows easy access as well as easy removal if I need the extra room for storage.
What size inverter do you have?