In this work, a comparison is made for the behavior of the total entropy generation and the total temheat destruction during a transient heat conduction process. A slab undergoing a 1D heat conduction is used as an example to illustrate the transient behavior of both entropy generation and temheat destruction rates. Formulations of the studied quantities are expressed mathematically and used to analyze the system. Next, plots of entropy generation rate and temheat destruction rate over time are generated. It was found that the entropy generation rate reaches a minimum before the steady state is reached. However, temheat destruction rate reaches a minimum only at a steady state. Additionally, causing a more dramatic temperature change in the system increases the steady-state value of temheat destruction rate, but it does not cause a minimum to appear before reaching the steady state, unlike for the entropy generation rate. The practical aspect and the application of temheat destruction minimization are in determining the steady temperature distribution in a complex geometry by minimizing the total temheat destruction through variational calculus or other numerical optimization techniques. Thus, this technique can be an alternative way of determining the steady temperature distribution in a given system.