One reason it may be important to match temperature is because in a much larger environment, fish can seek a different temperature if not comfortable.
As for the temperature of rainwater... this interested me so I started googling. My hunch was that rain water is colder than the air temperature and could have an impact on bodies of water... I thought this abstract was interesting (even if I don't understand all of it).
"The thermohaline response of the ocean to a short (10 h) but intense (95 mm) nighttime rainfall event was observed during a transit through the ITCZ. Two CTD profiles and shipboard measurements of air–sea fluxes were consistent with the assumption that rain temperature equals the wet-bulb temperature, within measurement errors. Although the net freshwater input and the net heat loss inferred from the T–S characteristics of the surface layer were ∼30% smaller than those obtained by integrating the measured air–sea fluxes, owing to different spatial sampling, inherent limitations of rain measurement from ship, and contamination by internal waves, the two independent estimates of the net heat deficit agreed remarkably well, within 2.4%, when expressed per unit mass of rain (∼72kj kg−1). The heat flux due to the temperature of the rain accounted for about 40% of the net heat flux during rain, and therefore cannot be neglected."
source: Flament, P., and M. Sawyer, 1995: Observations of the Effect of Rain Temperature on the Surface Heat Flux in the Intertropical Convergence Zone. J. Phys. Oceanogr., 25, 413–419.
As for why rain can be cooler than the ambient air temperature at ground, evaporative cooling came to mind. If you want to estimate the temperature of rain water, use the wet bulb method. We did this back in science class by taking a standard mercury thermometer and wrapping the bulb in damp gauze. When air moves over it, it will cool. By comparing that to the dry bulb temperature you can infer humidity. I think the greater question would be how much rain would it take to change the temperature of a body of water more than a few inches below the surface.