Avicularia, Poecilotheria, Psalmopoeus, and Tapinauchenius would survive reasonably well in a greenhoue which reaches temperatures of 90 maximum and 60 minimum. Given there is humidity and adequate food.
Many people so far have expressed concerns about the amount of food available to these animals, though I think the anticipation of a spider needing constant supplemental food is unrealistic. What's more concerning is depending on your location, the bare ground may be toxic to the tarantulas (mites, dryness, parasitic worms, and fungi). I think that this could be remedied with a ground cover like brick, tile, regular carpet flooring, plastic-- etc.
As for concerns that you will be interacting with this animal, the animal will certainly establish an area where it spends most of its time, this is the case for almost all scorpions and spiders. I can almost garauntee that you will not be stung or bitten by a scorpion or spider if you are aware of their den, burrow, or established area.
It may be true that these critters can escape, a scorpion may burrow itself out of the greenhouse, a spider, especially arboreals, can escape by crawling through extremely small holes relative to their body size.
However, given a large enough space these animals will, for the most part, be content in an area where food, water, and lack of disturbance are plentiful.
Making a greenhouse tarantula-escape-proof is going to be the hardest factor. How will you ventilate your greenhouse without allowing large enough holes for the spider to escape.
I would consider buying a burrowing species, and providing a suitable substrate for that spider to burrow in. With this method, you can see the evidence of the spider. A species that makes great burrows and intricate webbing (whom you may occasionally witness slightly exposed at the entrance) is Pterinochilus murinus. This species is highly defensive, however, it webs heavily, is easily available, and is relatively cheap. It is also sustainably available in the U.S. due to the breeding efforts of tarantula hobbiests.
If this tarantula is free roaming, I would consider altering part of your greenhouse to provide the suitable area for burrowing. This would serve a dual purpose:
First it would more or less gaurantee that the spider will establish itself in the designated spot.
Second it will reduce the amount of substrate (coconut fiber, long fibered sphagnum, processed peat mixed with sand or vermiculite).
It may also be more aesthetically pleasing, that is, the burrow would complex all along the area which you have placed the suitable substrate. And you would be less likely to ruin the critters home when you roam the greenhouse doing various things.