I don't see the need unless it's really long term storage (as in months) and even then I'm not sure it's worth doing.
I have a 40g storage tank that is translucent white for RO/DI. It's in the garage (in SW Florida... so it's hot 9 months of the year) and I don't circulate the water at all.
However, when I make up new saltwater I do 20g in a Brute and I mix it with a strong pump that really stirs up the water so it's well oxygenated when I use it for a water change.
I keep my mixing barrel in the basement fish room. Because I use the same barrel for both salt water for water changes and then refill with rodi for top off, I keep a small power head and a heater in mine so that the top off water is at the correct temp and well oxygenated.