Not necessarily. It really depends on what kind of film it is. For example, it is recommended to store Press and Provia 15'C and below.
For consumer films, it does make a bit of sense to put it in a fridge to extend it's usable life (in a way push back its expiry date); basically to retard even more the chemical breakdown process and stuff. Of course, that is only when you buy film and store them for more than a year... :sweat: