In plain English, colder air is denser. Denser air pushes back harder when the wing pushes down on it.

And for a good example of this in action, check out Delhi, India. Almost all the international flight operations are in the middle of the night, when the temperatures are mild, as opposed to the day when they are in the 100s.

As for redeyes, ATA, still has the Redeye out of SFO. Last time I flew an SFO-ORD redeye on united, they had two flights (a 777 and 757) and both had good loads. There is demand.

Currently ATA only has 2 daily flights SFO-MDW, while before there were many more. Perhaps Southwest played a role in encouraging retention of the Redeye as one of the remaining flights. (And both of the remaining flights are continuations of Hawaii flights)

Well, it works both way. If the air is denser, air plane will experience more drag, or air resistance that is why airplane cuises at high altitude. If consider taking off and landing, hot air is said more dangerous. I was told that PHX were subject to shut down if the day temprature is too high. I don;t know the details, but thought the hot air
is not warmed up evenly, it creates tubulance.