Not to be confused with "climb", a clime is a region known for its weather. In the dead of winter, we dream about heading to sunny climes, where we can hang out in shorts.
The key to remembering clime is that it's so similar to "climate," with which it shares the Greek root klima, "zone." So a clime is a zone that has a characteristic climate. Folks in colder climes think nothing of the kind of snowfall that we down here in the south get all panicked about. But then again, when they come here to our warmer clime, they forget to put on sunscreen; people from one clime can learn a lot from a visit to a different clime.