Equations

Here are some basic thermodynamic equations.

The First Law of Thermodynamics states that the change in internal energy is equal to the heat added to the system minus the work done by the system.

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/firlaw.html

From this it can be determined that energy is conserved, and if energy is conserved the internal energy of the system changes as heat flows in or out of it.

Therefore,

Qin=Qout

The heat in would be the hot plate underneath the coffee pot and the heat out would be the heat that is leaving through the pot and air. A combination of conduction and convection.