Lots of factors to take into consideration with that one.
Still cool air will not cool water as quickly as windy cool air.
Turbulant sections of river will cool quicker than still/slow moving section of river.
Rain can be warm or cool, and can fall on hot roads/warm earth and initially warm up until the soil starts to cool as the water runs off. (Think ground source heating that warms water).
Water running off or predominantly town/city streets will be a different temperature to that running off of mountainsides/fields.
But, I think it is fair to say a sudden, heavy and prolonged downpour would have a greater cooling effect than a cool day.