What your plant needs in the winter really comes down to two divergent paths: 1. dormancy (more accurately quiescence) or 2. active growth. I will describe each, and you can decide which works best for you.
1. Dormancy: Temp should be somewhere between 25 and 42. If temp goes lower than 25, there is a chance of tissue damage. Brief spells a little bit under will probably be fine. Extended spells well below may result in death of all the top growth, or even the tree itself. If temp goes higher than 42 for an extended period, it will start to push new growth, and drain resources. This can result in less vigor come spring time. An unheated garage is usually closer to this temperature range than a basement, unless you have a very cold basement with a lot of cold air infiltration. You will want to make sure the soil in the pot does not dry out completely, which means putting a bit of water on it once every month or two. Evaporation occurs very slowly at these cold temperatures.
2. Active growth: If you want to try to keep a fig tree as a house plant, this is certainly possible. It will do best if it is in a south facing sunny window and gets at least 8 hours of direct sunlight per day. If you keep it inside, but don't give it much light, this will weaken the plant because the photosynthesis taking place will not keep pace with energy expenditures by the plant (leaf/stem growth, transpiration, etc). The plant may survive but will not do as well as if you had let it go dormant. Regular household ambient lighting is not enough, it needs to be either direct sunlight, or high wattage grow lights.