The cup of water will be at room temperature by morning. It will not be any colder or warmer, if the room gets cold so won't the cup of water, but it wont be sudden, it will gradually become room temperature as it did in the beginning. For example: If you have a cup of water that is cold, and you leave it in a room just as in the question, by morning what do you think will happen? Will it be colder than the room it was left in? Will it be any warmer? No. It will be the same temperature as the room that it was left in over night. If the room is cold then the cup of water would also be cold but the same temperature as the room itself. Think about it. Have you ever left something like a glass of water or milk out in a warm room? When you come back isn't the water or milk warm just like the room? Yes it is xD \\\\ So, for this answer. The cup of water will be at room temperature. Some may have also evaporated. The water cycle is a never ending thing, Water is always evaporating no matter where it may be, or how it may be.
I Hope This Helped!
