Putting a constant heat source in a closed container, will the temperature grow increasingly hotter?

i want to build an incubator out of a cheap styrofoam container for leopard gecko eggs. I want the temperature to remain in the high seventies low eighties. i planned on hooking up a dimmer switch to a piece of heat tape which will produce a constant heat output, but if i put it in the styrofoam container and leave the lid on will i be able to keep it that low and have it stay constant or will the temperature of the air in the container grow increasingly hotter if there is no air flow/exchange?