In this study, we investigated the effect of Cr doping on CuMn2O4/CuMnO2 and established an oxidation (heat release) kinetic model for CuCrxMn1-xO2 (x = 0, 0.1, 0.3) as an extension of our previous research on developing medium-high temperature (500–1000 °C) redox-type thermochemical energy storage materials. Our objective is to develop a reliable model for predicting the heat release power at constant temperature conditions. The as-prepared samples were characterized using XRD Rietveld refinement, SEM-EDS, and XPS analysis to obtain a more precise crystal structure and elemental states. The oxidation kinetic model was established using an isothermal oxidation method which differs from the method (non-isothermal) used in the previous study. Additionally, the pressure term was also taken into consideration. The reaction models and kinetic parameters of CuMnO2, CuCr0.1Mn0.9O2 and CuCr0.3Mn0.7O2 were determined using master plots and Arrhenius plots. Among all sample, CuCr0.1Mn0.9O2 exhibited the smallest oxidation activation energy of 29.932 kJ/mol, which was significantly lower than the previous value obtained using the non-isothermal method. Combining the reaction rate and heat release, CuCr0.1Mn0.9O2 showed the highest instantaneous power output of 4.69 kW/kg at the oxygen partial pressure of 0.5.