Would a sloth survive later on

The sloth in say, 5,000 years into the future with the world having more climate change problems than in the current world would be a NIGHTMARE for the sloth. If the world got colder, then sloths would not be able to finish reproduction because in order for the sloth to give birth to its offspring, it needs really warm weather like from 72-97 degrees fahrenheit for a mother to give birth to its offspring. Since the sloth is super slow, and there might have predators adapted to the cold migrating to the rainforest since it got colder, then the predator and its pack would prey on all the sloths, the sloth would be extinct in 5,000 years if there is many climate change problems.