The work done in order to transfer the heat from a cold body to a hotter body is in fact the work done to "ABSORB THE HEAT "from the cold body to transfer it to the hot body.Is this correct?
Heat always flows from hot to cold. Heat does not flow from a cold object to a hot object. For example the heat from a hotplate passes into a cold pan to heat up the water in the pan.
The greater the temperature difference between the hot object and the cold object, the greater is the flow of heat