The optimality in heat conduction processes in solid materials is studied analytically. Based on the second law of thermodynamics and the definition of entropy a new thermodynamic property, temheat, is introduced. A balance equation relevant to temheat is derived by modifying the entropy balance. Principle of temheat destruction minimization is applied to several steady heat conduction problems. It is shown that for all steady heat conduction problems, the thermodynamic quantity, the rate of total temheat destruction, is always minimized. The principle of temheat destruction minimization helps to better interpret the natural heat conduction phenomena and to obtain numerical solutions in heat conduction problems. ©2011 Academic Journals.