The exchange will remain until the two bodies are at equal temperature. In a calorimeter , heat is exchanged between the water and materials undergoing change. So heat gained or lost by water can be calculated. Upon using this data, one can determine the heat lost or gained by the materials undergoing change, and in this case it is ice. Be very careful when removing the un-melted ice so as not to remove any water with it.
Any water left in the graduated cylinder is a source of error.
Go to the vocabulary list as a useful reference guide to new vocabulary words that need clarification. Various heat transfer and fluid flow homepages. All one would ever want to know about energy and its functions and purposes with numerous links.