cage heating question- need advice

[Will0W783]

I just bought a bunch of melamine snake cages this past weekend, and I need to know how best to heat them. They are 5'x2'x2' and 6'x2'2'. They stack on top of each other, so I think heat lamps are out, unless I mounted them sideways to the doors and I'm afraid that would start a fire. The doors are vented plexiglass and wood. I was thinking of Flexwatt heat tape, but my question is, would that go on the inside floor of the cage, or underneath them? It's pretty thick melamine, so I can't imagine that heat would pass through the floor up into the cage, but if I put the tape inside on the floor of the cage, would it burn the snakes? Right now I have a heater in the room getting the ambient temperature to 85 during the day and 80 at night, and I have a floor lamp with 3 telescoping bulbs providing light and a window. I know I need to come up with a more efficient and permanent way of heating these things. Previously I just had aquariums with screen lids and heat lamps. Any advice and help would be most appreciated.