why does water heat up faster over a longer period of time?

Answer 1

It's doesn't. It just seems to heat up faster as time passes because the water molecules are becoming more energetic with the constant addition of heat, until they hit the boiling point and start to change phase from liquid to gas vapor.

Answer 2

Water does not "heat up faster over a longer period of time."

If water heats up quickly (fast), it does not happen over a long period of time. A long period of time is a definition of "slow". Fast can be defined as quickly or over a short period of time.

Regardless, it should be noted that relative to, say, vegetation or the air, water heats and cools very slowly. In the beginning of summer, it is common for rivers, lakes, and especially the ocean, to be very cold even when it is very warm outside. This is because water's temperature is very slow to change due to its Specific Heat Capacity

Other interesting, related topics are:
* The Mpemba effect, which is in regard to the phenomenon where by hot water freezes faster than cold water.
* Hot ice, where by applying electricity to ice, it may maintain a solid icy state even at room temperature. (perhaps this is somehow related to the Mpemba effect?)