The history of the universe is a history of entropy liberation, which means, simply, that entropy increases. But what does that mean?
Many sources will tell you that the increase of entropy is dissipation[1], degradation, and dissolution, and they're right, but they're not entirely right. It is a glass half empty/full sort of situation, for along with the dissipation, degradation, and dissolution comes everything else.
So when a warm body simply gives heat to a colder body, yes, some amount of potential work has been lost, but some body, some where is warmer, and that increases entropy.
The entropy liberation front is where everything happens, because nothing happens without the liberation of entropy. Things can stay the same without the liberation of entropy. But for change to happen, entropy must be liberated.
[1] See Lord Kelvin's papers and lectures for instance: "Although mechanical energy is indestructible, there is a universal tendency to its dissipation, which produces throughout the system a gradual augmentation and diffusion of heat, cessation of motion and exhaustion of the potential energy of the material Universe"[Source]