A non-steady heat conduction equation based on mass co-ordinate was derived for a slab, which is convenient forconsideration of temperature dependent physical properties. Its integral form was then expressed using the differential ratio of the zero and the 1 st moments for enthalpy distribution, which provides additive relations of the internal and the surface thermal resistances. Numerical solutions for the heat conduction equation are obtained using linear temperature dependences for (thermal conductivity times density) and (integral average heat capacity), for various Biotnumber. A model equation with three parameters was applied for profiles of temperature and enthalpy. The relation between the zero and the 1 st moments of the enthalpy distribution were well correlated by the empirical equation previously reported for the concentration distribution in desorption process. The integral form of the heat condution equation with the two above relations was applied for inverse problems of calculating temperature dependent physical proper-ties and surface temperature dependent heat transfer coefficient from measured temperatures in a slab. Illustrations are shown for calculation of surface temperature dependent heat transfer coefficient on the water-spray cooling of a heated steel plate.