Temperature is what ripens toms, flowergirl. If it's warmer outside than in the shed, they will ripen quicker outside. If the converse is true, the converse applies. Hanging up the plant is really only a means of storing the toms. Out of the ground, the plant will die off within three or four days anyway so there will be no ongoing nutritional benefit.
EDIT. If it's not warm enough outside - and you need at least low-20sC for ripening at an optimum rate - put them anywhere where you'll achieve as close to those temps as you can. In a shed, in the kitchen, bathroom, boiler room, wherever.