The term heat refers to the flow of energy.
If you drank a cool drink, it would only cool you down the difference in temperature for that amount you drink.
The liquid is brought into your system and therefore will warm up to your body temperature, while your body correspondingly cools down a little bit.
Different materials have different specific heat capacities so something like lead will heat up much faster than water.
The lead will also cool down faster while the water retains heat for much longer, this is partially related to hydrogen bonding in water.