Because it is an ideal environment, external influences are not taken into account.
And because the specific heat capacity of water is constant (that is, the energy required for water to rise from 0 degrees to 10 degrees is equal to the energy required for water to rise from 80 degrees to 90 degrees).
So, if the water temperature is used to carry out work, then cooling 10 liters is twice as fast as cooling 20 liters (energy loss should be equal to that of 20 liters).
If water is used for heat conduction, then when the temperature of the lower temperature medium is constant, both will be equally fast.