If your fig tree has already received some chill has "understood" perfectly well that the cold has arrived, so the leaves, as it should be, have fallen.

Where is the problem??
It has not to make any leaves until spring, it is at all normal.
Figs fruits will not ripen on the branches, and you can remove them.
DO NOT KEEP the PLANT IN HEAT, light is not necessary till in spring, the temperature must be less than 40-45�F, so is better in a garage or in a cold veranda in range 28-45�F; if the temperature is above freezing, keep the soil moist (a glass of water once one week or twoo).
If the plant for heat breaks dormancy is a trouble!!!.
With cold (in said range) and dark the conditions are perfect.
Questions like yours are repeated every year, and the answers are always the same.
Do not forget the watering....,

Thanks for the suggestions. My concern about the garage is that there is no heat at all in our detached garage. Will it be a problem that the temperatures will dip into the teens or lower for weeks at a time?

Here in Missouri my fig trees will go dormant till late February. I keep mine in a green house so lighting isn't a problem.
Don't forget to keep them watered.
You could set them outside on warm afternoons after they start to leaf out, just don't let the new leaves get frost on them.

The cold, even several degrees below freezing, is not a problem. If the temperature drops much below freezing, supports the pot on the floor, NOT next to the cold walls, and completely cover the tree and pot with paper. The light is NOT necessary if there are no leaves.
It is better to keep it cold, that does not make the leaves. Put it in the light and warm when the large cold is over, eg the end of March. Check: If it start to put leaves in the garage, put the plant outdoor, in warm sunny site.

Dbay - get a cardboard box large enough to cover your tree. Put your tree directly on the floor & cover with an overturned box during extreme cold & all will be well. Every month or so, check the soil for moisture. It should be barely moist. If it seems too dry deep in the pot, toss a little snow on the soil (or water to dampen) & put the box back in place if necessary. The box is only necessary during periods of extreme cold where it's likely you'll see actual root temps at Al