I personally use the lights in the room and that come thru the window for light in my snake room. For heat I use heat pads with a Thermostat. I would return both light bulbs and order a heat pad and a thermostat from reptilesupply.com. With shipping it would cost you less than $40.00 and would be well worth it. Plus the mats dont dry out the air and warm air will hold more humidity that cool.
Just my 2cents. Good luck with your baby!