Non-equilibrium thermal response of polymers at nanosecond and longer time scales is described by linear differential equations with dynamic heat capacity in the framework of the linear response theory. The equation can be utilized on the length scale of more than 10 nm for semi-crystalline polymers and down to the nanometer scale for amorphous system. Self-consistent analytical solution for non-equilibrium thermal response of polymers under pulse heating in planar and spherical geometries is obtained. Non-equilibrium thermal response of polymers under pulse heating differs significantly from the thermal response of materials in equilibrium. It is noteworthy that even very fast components of the dynamic heat capacity (with relaxation time in the order of 1 ns) significantly affect the thermal response to the local thermal perturbations (at nanometer scale). This can be significant for the heat transfer process at fast formation of crystallites on nanometer scale.