Probably nothing would happened except the plant would grow faster and bigger. However, if it were to be watered too much the plant could develop root rot and die. Greenhouses in my area of the desert frequently grow desert plants for sale,
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The desert is usually not humid unless it happens to be during the rainy season. I live in the desert and yesterday our humidity was 2% with a dewpoint of minus 26 degrees F. That is about as dry as one can find.
If anything, the plant or animal might live a bit better off as a grassland receives more rainfall than a desert. There are a number of plants and animals that already live in both the desert and the grasslands.
Carnivores, herbivores and omnivores might share a desert habitat.
Arizona is in the Southwestern region of the United States of America. There is no desert named "Arizona Desert" might have been confused with Sonoran Desert which is also in he Northern part of Mexico.
This is an example of a metaphor. A metaphor is a comparison to show how two things are similar. That would be metaphor, if the area really isn't a sauna. Metaphor is naming something to be something other than what it is, usually for emphasis or better description. For example you might step into a greenhouse and say, "Wow, it's really hot and humid in here!" A greenhouse is not a sauna, but if you say, "It's a sauna in here!" you are emphasizing the heat and humidity -- and with fewer words.