Put cat in on hot nights or leave him out in his carrier

So who is right? It is 90 at night here and until the heat wave we kept Henry, an outside cat, in his carrier on the porch at night. Even though he is neutered we don't want him to run the woods at night.

Now that it is so hot I want to bring him in with his carrier at night

My wife says leave him out on porch all night because the AC in house will hurt him in the daytime.

Who's right

Bring him in. At least he will be comfortable for a while. It won't make any difference to him in the daytime, but it would be better to keep him in then, too.

Rose we live in the country and have 3 acres horse fenced. We also have two inside/outside cats and two inside... The limit of my wife's allergies.

Henry does fine with the run during the day and carrier at night for several months but this heat is a new wrinkle.
My wife feels the ac will hurt his tolerance for the daytime heat. I know people who work outside try not to use ac because they say it hurts them in the daytime heat.

I'm not sure for cats so I need opinions