When I first saw SA it was thinking South America, not South Africa, but both are south of the equator so it is summer. What temperature do you consider "very hot"? That can be so subjective, what is hot to some people is not to others. The actual numbers matter.
With your information I generally agree with the others. Move them into the coop and leave them locked in the coop for a week or so to get them used to it being their home. Then open the door to give them access to outside.
The rule of thumb is one nest for every four hens but I like a minimum of two even with fewer hens to give you some flexibility. It will not hurt to have more but all you need is two nests.
The minimum recommended size is 30 cm x 30 cm. This should fit any size hen, from a tiny Sebright that might weigh less than 1 kg to a Jersey Giant that might weigh 5 kg. I made mine 40 cm x 40 cm because that fit my coop framing.
When they lay the hens "stand up". Not much but a little bit. When they lay a small section of the plumbing extends out of the vent a small amount, maybe 6 mm. So they raise up enough to keep that exposed part out of the nesting materials. If you put a cover on the nest 30 cm should be plenty high, even with a lot of nesting material in the nest.
How about this instead. These are old threads but they show you some of the things we have done. As you can see there are no rules as far as the chickens go. Some people have a lot of flexibility and a sense of humor. Mine are in the first thread, post #64.
Nest boxes
https://www.backyardchickens.com/t/41108/show-us-your-nest-boxes-ingenous-design-post-it-here/220
Nest Boxes
https://www.backyardchickens.com/t/...-your-creative-nesting-boxes/80#post_12395882
Good luck!