If the lighting fixture is rated for 60 watts, 75 watts, etc.. Is this based on a incandescent bulb or a CFL? Does a 60 watt CFL burn as hot as a incandescent?

Yes the ratings are based on incandescent bulbs. If you use a CFL that gives as much light as a 60 watt bulb it will be significantly cooler. Did I understand your question correctly?

Does a 60 watt CFL burn as hot as a incandescent?I think Ballen understood you.

I'll just say that a 60W CFL would be huge. About 10" long and 4" wide.
CFL's are rated in their actual wattage, NOT their equivalent wattage.
A 13W CFL is about as bright as a 60W incan, but it is still only a 13W lamp.