Among the laws of physics, only the second law of thermodynamics distinguishes a preferred direction in time. This thermodynamic arrow is commonly expressed in terms of entropy increase toward the future. An equivalent formulation is Clausius’s statement that heat energy flows spontaneously from hotter to colder bodies. It is tempting to suppose that reversing time would simply reverse this process, such as watching a film backward, with heat energy flowing from cold to hot and thermodynamic evolution retracing earlier states. In this paper, we examine that intuition within classical thermodynamics. Drawing on earlier pedagogical and technical analyses, we argue that reversing the direction of spontaneous heat flow does not produce a reversed thermodynamic evolution. Instead, temperature differences amplify, equilibrium ceases to function as a stable endpoint, and thermodynamic description breaks down. In this sense, the thermodynamic arrow of time is structurally irreversible. This paper is aimed at the undergraduate level.