Carnot discovered that the efficiency of an ideal process depends only on the temperatures.

By brilliant abstract thought the French physicist who developed the theory of heat engines in Réflexions sur la Puissance Motrice du Feu (Reflections on the Motive Power of Fire) (1824) perceived that temperature provided the key.

He realised that the difference in temperature levels is what determines the amount of work that can be obtained from flow of heat. He proposed the reversible Carnot cycle, and discovered that the efficiency of a heat engine depended only on its input and output temperatures.

For Refrigeration, what is the minimum amount of energy necessary to raise the temperature?

Carnot was not completely right, because heat cannot be thought of as a substance which is conserved like Caloric. The same amount of water flows away from a water wheel as enters it. But we now know that less heat flows away from an engine than is put into water in the boiler.

An Englishman called Joule showed what had happened to the lost heat. It had turned into work! This discovery, and the subsequent pioneering work by Clausius in Germany and Thomson (later Lord Kelvin) in Scotland resulted in the Second Law of Thermodynamics, which tells us exactly how much of the heat it is possible to turn into work.

And by implication, this tells us also the minimum amount of work, or power we must put into a refrigerator to make the heat flow from the low temperature level to the high temperature level.