Was it Mythbusters who tested that idea of cold gas giving more bang for your buck?
If memory serves, since fluid density is less affected by temperature than gas (the state of matter,) and gasoline is stored underground in tanks which tend to stabilize temperature compared to the heat or cold we feel when fueling up, it doesn't really make a statistical difference.
I don't remember them trying that one, they did all other kinds of fuel efficiency myths though. I might be conflating the don't pump when the tanks are being refilled with cold v warm.
I may also be just assuming any clip I vaguely remember testing any urban legend whatsoever must have been Mythbusters the way every song parody on Napster or LimeWire was labeled as "Weird Al."
I remember my dad saying to avoid getting gas on the really hot days because the heat makes the gas evaporate faster to fumes. Now how much difference does it actually make? Who knows. But that was my recollection of the"why" behind it.