I have some texas everbearing figs in pots that I place in an unheated shed during the winter. I do this because pots are not good at protecting the roots from a hard freeze. Also, a winter freeze tens to damage some pots, depending upon what they are made of. If you are going to move it back outside, I would wrap the pot in insulation or plastic stuffed with straw to help protect those roots from a hard freeze.

Jumping from a 3 gallon to a 15 gallon pot might be too much.

Until the roots grow a lot to fill up the 15 gallon pot, you will have soil on the sides of the pot that stays wet, since no roots are absorbing it. This can cause problems.

I'd say go from a 3 gallon to maybe a 7 gallon at most.

Just my 2 cents.