The variations of the heat storage and heat transfer properties such as heat capacity, thermal conductivity, and thermal stability of Platinum electrode for oxygen sensor with temperature, time and grain radius are studied by using the theory and method of solid-state physics, and the effect of anharmonic vibration of atoms on the heat storage and heat transfer properties and the thermal stability is discussed. The results show that the heat capacity of Pt electrode first increases with emperature, then tends to be constant, and decreases with grain radius and time. The thermal storage stability coefficient of the electrode material increases sharply at first and then decreases rapidly with temperature, and finally tends to be constant. When the temperature is about 60K, the thermal storage stability is the worst. The thermal conductivity of Pt electrode material decreases sharply at first and then tends to be constant with temperature, increases with grain radius, and decreases with time. The contribution of the surface layer to thermal conductivity decreases sharply at first and then tends to zero with temperature. The anharmonic effect of the electrode material reduces the heat capacity, while increases the thermal storage stability coefficient and thermal conductivity. The results obtained in this paper are basically consistent with that in other literatures, and the conclusions can provide theoretical guidance for the stability of solid electrolyte oxygen sensors.