I have repeatedly said my first egg cost me $650. These days they cost me about 3¢ per egg. But if I had to keep replacing Tractor Supply coops every 5 years that cost would be dramatically higher. We were donated one of those coops. Occasionally I do an inspection and have to replace parts of it with scrap lumber. Coop of Theseus. I have replaced exactly one piece on the 7 other coops I've made over the last 9 years. Not one part each. One part total.

I advise every first time chicken tenders to make the best coop they can instead of buying off the shelf. Even if that coop is literally pallets and hardware cloth held together with rachet straps and door hinges they pulled off a door of the local dump. It will last longer than a Tractor Supply coop.

It does not look like much in the way of materials, but it all adds up fast!

You probably could have gone down to tractor supply and picked a kit for $400 or so, but it is made of wood only slightly thicker than cardboard and would not have the open floor.

I need to do something like this for my cat who wants to be an outdoor cat.

Correct. Which is why I installed vents.

The plans I based this on had a considerably smaller vent. One. Making matters worse it had windows. Glass windows. An absolute nightmare of cleaning and heating waiting to happen. I quickly nixed the windows and instead of just one vent on one side I put in two larger vents, one on each side. I also reduced the depth of the roost by about 40% to save on materials. This also means that the larger vents I installed are way more effective than they need to be. In fact I might have to build vent covers for extreme winter night lowes but that is for another day.

The only time hens will be in there are

1. overnight (temps are never over 86 overnight in this area) or when laying eggs.
2. If they are laying eggs they won't be in there long.
3. they are broody. Any heat might help break them of that.

Bonus: the original plans had insulated walls with foam board. The combination of tiny vent, two windows and insulation would have cooked everything inside.

TL:DR The hotter (less dense) air will rise. It will leave via the vents or get tapped up much higher than the birds or the vents. I'm not worried at all. Adding more vents would be trivial but are ultimately unnecessary.