Perfect- just remember to say “it cools off at night”

You would say “the temperature drops at night” or you would say “it cools off at night” where “it” is our general way of describing the weather.

Great example, but pay attention to one thing. This is a common (and sometimes funny) mistake in English. When you use an adverb like “impatiently,” you want to put that word closest to the action that it describes. In your sentence, you have two actions: (1) waiting and (2) cooling off. You placed “impatiently” closest to “cooling off.” So the sentence now implies that “the weather will cool off impatiently.” Actually, the weather just cools off; your cat is waiting impatiently.

So you want to move the word “impatiently” closer to the action it describes, which is waiting: “My cat is waiting impatiently for the weather to cool off.”