Why does heat not spontaneously flow from a colder object to a hotter object?

The observation that heat does not spontaneously flow from a colder object to a hotter one is a fundamental principle described by the second law of thermodynamics. Specifically, the Clausius statement of this law asserts that a cyclic transformation whose only final result is to transfer heat from a body at a given temperature to a body at a higher temperature is impossible.12

This phenomenon is statistical in nature. At the microscopic level, individual molecular collisions are time-reversible, meaning there is no fundamental law preventing cold molecules from clustering together. However, because macroscopic objects contain an enormous number of molecules (approximately ${10}^{24}$), the probability of such a spontaneous, organized collection of cold molecules is so exceedingly low that it is never observed in practice.13

Instead, heat transfer is governed by the requirement that the net entropy of an isolated system must increase or remain constant. A spontaneous flow of heat from a colder region to a hotter one would result in a negative net entropy change, thereby violating the second law.1