If you are having trouble removing the prints after cooling, then there is a much stronger chance your suggestion would work. With glass beds, once the print has cooled, with no other adhesive involved, the part is a simple lift removal. Some users/printers have no heated bed and use blue painters tape or spray on adhesive on a cold surface.

I should have considered to ask if you were using adhesive. You may get away with a cooled bed after all.