What if Energy Flowed from Cold to Hot? Counterfactual Thought Experiments

What if energy flowed from cold to hot regions? How would thermodynamics be different? We examine such an imagined cold-to-hot world, abbreviated here as a C2H world, and show that the unfamiliar direction of energy flow implies that two thermally interacting objects at different temperatures will not equilibrate. We find that there is no operational definition of temperature, and the first, second, and third laws of thermodynamics become meaningless.