They wouldn't be POLAR bears. We have bears here in Phoenix that's the desert
Why don't polar bears live in deserts?
They don't.
For the same basic reason Grizzlies don't live in the Artic region. They are not suited to live in hot dry places with those huge fur coats that help them survive in the frozen tundra but would kill them in the desert heat thus Grizzlies can survive in less colder temps, they could not survive long in Polar Bear regions. But the we have the Chicago Bears who are just trying to survive season after season but never get a winning season anymore, sorry couldn't resist here
I read that the polar bear, the king of the Arctic, is considered by many to be a marine mammal, since it spends most of its time on sea ice hunting for seals. There are no seals in the desert!