Well, when it gets really hot, I usually sing:
(Bring Me Little Water,) Sylvie
and
Cool Water.

There's also
(We're Having A) Heat Wave

For rain songs, there's:
Early Morning Rain
Rhythm Of The Rain
Raindrops Keep Falling On My Head
Singin' In The Raid
Who'll Stop The Rain?
Have You Ever Seen The Rain?
and the Ladysmith Black Mambazo song, "Rain, Beautiful Rain"