If you’re looking forward to lots of outings with your partner, take a look at these details about year-round temperatures in Fall River: The hottest months are usually August and July, with an average temperature of 17°C, while the coldest months are February and January, with an average of -1°C. The snowiest months in Fall River are February, January, December and November, with each month seeing an average of 60 cm of snowfall.