There's a lot of good advice above. I think there are three issues:
1. Is it useful to keep figs warm during winter? My own opinion is that it isn't, consistent with comments by TorontoJoe.
2. Is it useful to get figs warm early in the spring? Here I think the answer is yes, within limits, consistent with the comments from Calvin. From my own observations of my inground figs, bud break seems to come roughly 7-10 days after a prior 7-10 day period of warm weather. So if you can move quiescent figs from cold storage into a warm room before it is warm outside, you might get a 2-3 week jump on the season -- without a shuffle. But without strong sunlight, any foliage is likely to be sensitive and the transition to outdoor conditions might set the figs back somewhat. So I think you'd want to move the plants outdoors into warmish weather soon after bud break.
3. Is it useful to keep figs warm in the fall? Here too I think the answer is yes, within limits. As Calvin suggests, you might ripen extra figs for a few weeks. But remember that any figs that will be stored in cold conditions need to acclimate to the cold. That takes time. The longer you store the figs in warm conditions, the shorter and tougher the transition to the cold.
FWIW, my wife and I added a sun porch two years ago, and we love it. It is not heated at all, so we don't use it in the depth of winter. But sunlight warms the room enough that we can sit "outside" on cool days and evenings in early spring (March - May) and also late fall (October - December). [My sister slept in the room one night last November.] And when it's warmer (June - September) we use shades, ventilation and a fan to keep temperatures very comfortable. Screens keep out the bugs.