The internal heat loss or cooling of a planet determines its structure and evolution. We address in a consistent fashion the coupling between the day and the night sides by means of model atmosphere calculations with heat redistribution. We assume that a strong convection leads to the same entropy on the day and night side and that the gravity is the same on both hemispheres. We argue that the core cooling rate from the two hemispheres of a strongly irradiated planet may not be the same and that the difference depends on several important parameters. If the day-night heat redistribution is very effective, or if it takes place at a large optical depth, then the day-side and the night-side cooling may be comparable. However, if the day-night heat transport is not effective, or if it takes place at a shallow optical depth, then there can be a big difference between the day-side and the night-side cooling and the night side may cool more effectively. If the stellar irradiation gets stronger e.g. due to the stellar evolution or migration, this will reduce both the day and the night side cooling. Enhanced metallicity in the atmosphere acts as a blanket and reduces both the day- and the night-side cooling. However, the stratosphere on the day side of the planet can enhance the day-side cooling since its opacity acts as a shield which screens the stellar irradiation. These results might affect the well known gravity darkening and bolometric albedo effects in interacting binaries, especially for strongly irradiated cold objects.