Last year was my first year with figs and I asked a similar question. I had babies that I was worried wouldn't survive dormancy so I built a little indoor greenhouse with a clear plastic bin, heating elements, LED grow lights, etc. At first it worked great, and I saw similar results as reported by Danny. Then the plants outgrew the greenhouse and I tried to extend by using plastic wrap. Unfortunately the plastic wrap was a poor insulator and the heating elements didn't do their job in the colder months or the plants were overcrowded. They slowly lost their leaves 1 by 1 and it was a project to keep them alive. I keep the spare rooms at 60 degrees in the winter. Then there was the fungus gnats! They were controllable with sticky tape, but there was always a few flying around and it drove my wife nuts.
In Spring, the weather warmed up to 65-70 and I took down the greenhouse and began moving them outside during the day and inside at night. Well the 2 older plants I let go dormant woke right up and started sprouting leaves. The greenhouse plants went into shock and lost all of the remaining leaves and stayed that way for a couple weeks for the good ones to almost 2 months for the stubborn ones. I thought my Smith plant was a goner until it started sprouting leaves in mid-July. Now its October, all plants have recovered and grew tall, but all of the greenhouse plants have tons of immature figs due to the late start. I don't know if the baby plants would have survive the dormancy, but this winter I am going to let my baby fig plants go dormant and see what happens. I think if you have mild winters (Texas) or keep your house warm and are extremely careful about weaning your plants from grow lights to natural light, it will work, but there is a lot that can go wrong.
Good luck,
Andrew