As others have noted, higher tensions and stiffer strings in heat with
increasingly less tension in cooler weather.
As one moves into cold weather (like unheated indoor clubs), it typically helps to switch to softer strings -- there's only so much "give" some stiffer poly's have in cold weather. Going to softer strings can mean going back to higher tensions, or not, depending upon personal preference and experience.
Expect to restring more in cold weather. Hitting a ball at 45 degrees indoors in the winter is much tougher on strings than 90 degrees in the summer sun.
Also, it can help to take a short pregame visit into the Club's dry sauna with the racquets in cold weather to warm strings and frames up.
A short preplay visit into a hot dry sauna is also a good way to quickly 'break in' a new pair of tennis shoes. Let the shoes sit around in the hot sauna 5 or 10 minutes before putting them on (put them in the sauna before you get your tennis gear on). The heat of the sauna will help shape your new shoe's footbed to match your feet for quicker comfort than you might otherwise get playing.