I'm more into boas so I don't know much about egg incubation but a small to mid sized closet seems like a lot of space to keep at a steady temp but I guess the space needed depends on how many eggs you have. It sounds like a decent idea but I'm not sure you could leave a bathroom ceiling heater on for long extended periods of time. I use a heat panel i got from boamaster.com to keep my enclosures at the temps I want, maybe you could use one of them. I honestly don't know much about egg birth etc but just figured I would throw it out an idea that may give you more option or whatever. Either way Best of luck, keep me posted on what you decide I'd like to see how everything turns out.
http://boamaster.com/products/120w_Heat_Panel-11-1.html