Like humidity, temperature is extremely important for your piano performance:
Changes in temperature will affect basically the metal structure of your instrument, and that includes the strings. When warm strings expand and pitch goes down, when cooled strings contract and pitch goes up, and because they are not the same length If the piano was tuned at 76F it will go out of tune at 80F and it will also sound out of tune at 72F.

Constant changes of temperature will greatly help loosing the tuning of the piano and will make the instrument unstable. If this condition is maintained for long period it will even shorten your piano life the same as humidity does. Ideally, the temperature should be kept even all year long, between 74 oF and 78 oF.