Tuberous begonias seem to have very specific needs, Cinta. I'm not sure what will be the best way to overwinter yours since it's in with others -you'll probably need to remove it from that pot, unless the other plants get a winter rest period?
Things tuberous begonias want:
-Warmth; both soil and air. Critical in the early stages, but once blooming they can take cool weather as long as their leaves are kept dry.
-Fast-draining, but moisture-retentive planting medium. I use straight compost these days and water infrequently.
-Leaves dry almost 100% of the time to avoid disease. This means that attention is required throughout its growing cycle. If the lower leaves start touching the planting medium, pinch them off. If they look discolored or misshapen, pinch them off. Once disease gets going it's almost impossible to reverse in the same season.
-Fed at every infrequent watering. I alternate between two food types; one has a high phosphorus rating, the other has micro-nutrients and a higher potash rating. (These are my standard fertilizers...I don't keep special ones on hand just for begonias.)
-High light levels, but no intense sun. Early and late in the season they'll want a bit more gentle sunlight than what they can tolerate in high summer.
-Humidity; plants kept indoors over winter often don't get as much of this as they need.
At the end of the season I allow my potted plants to stay outdoors until the cold finishes off this year's growing season, and then allow the planting medium to dry out. Once the pots are very light, I store them in a spot that will cool down right along with the season, but remain unfrozen.
The other way to overwinter is to remove the tubers from the medium, allow to dry, then store in vermiculite or dry peat in a cool, dark place for the duration. (Personally, I experience more losses from mold and rot this way, and prefer the other method.)
This year I didn't get my tubers out until after July 4th, much later than normal, and they preformed better than ever before. I just set the pots out of direct sun and hung them up once they filled the pot. I don't even recall giving them water/food until they'd started showing growth.
Pictures taken this morning after two weeks of nights in the forties (but dry, under an opaque roof), and they're still holding on.
(The scraggly and spent plant hanging behind the red one is one that was started early in a nursery.)
Hope some of this helps.