SrHfO3 (SHO) is probably the leading gate oxide for the Si chip industry. The material is processed at ∼400 K and annealed at high temperature ∼1600 K. Unfortunately there are two phase transitions in SrHfO3 in this temperature range, which can affect the quality of the final films processed, especially their channel mobility in SHO-based n-FET. To clarify these transitions and their impact on SrHfO3 processing, we report the temperature dependence of soft phonon modes by Raman spectroscopy. The 1023 K Cmcm-I4mcm transition is found to be displacive (no disorder) and nearly second order. Significant effects are also seen in the orthorhombicorthorhombic P nma-Cmcm transition at 670 K.