If you get "blistering hot" weather 2 months out of the year, how will you ventilate and cool your green house?

Unless you lay a concrete floor, rabbits and their ilk (such as skunks) will just dig under the walls and eat your veggies anyway.

Laying hardware cloth at the bottom of your beds will keep most digging vermin out. It should extend beyond the edges of the raised beds by at least a foot so they can't push it up at the edge when they dig under. The one time I built a bed like this, I actually stapled it to the outside of the beds so it was a continuous barrier with no gap between the bottom of the wall and the barrier. Overlap joins at least 6". Cover with dirt inside the beds.

Garden fencing will keep most pests out from the top. If your raised beds are 4' wide or less, deer generally will not jump the fence. They may nibble at anything that sticks through it though. Make sure it is something a deer can actually see - as I recall they are color blind and there are only certain colors that will show up to their black and white vision very well. I don't remember what the best color for fencing is for them to see it, but as I recall it was something that I would never have guessed. Green maybe?

Your best bet is a good farm dog who will stay on the property. Either fence all the way around your house and garden or train the dog to STAY HOME. I had a border collie mix who knew exactly where the property line was and WOULD NOT LEAVE, very unusual for a dog I admit - but she kept the deer, coons, rabbits, and everything else out of the garden - and stayed out of it herself after the first couple of NOs from me. I still miss her.

But anyway. Fence the garden in, then fence around all that with wire fence and T-posts - and let the dog loose in the yard. Critters won't come back once they know there's a dog. Just make sure there's plenty of human contact, shade, and water for the dog. A terrier or other digger is probably not your best bet - but there are any number of breeds, crossbreeds, and mutts that could make a good farm dog and helper.