A modified Duhamel's theorem developed previously requires a normalized temperature response function of a body of conduction heat transfer. Empirical response functions based on parameters f and j were used in the theorem application since many foods were irregularly shaped and analytical response functions were not available for such foods. Using this theorem, 30 analytical formulae were derived to estimate the temperatures of foods undergoing several different heat transfer processes with two- or four-step functional changes in heat exchange medium temperatures and convective surface heat transfer coefficients. Sample applications for these analytical formulae include determination of the j value for the cooling phase of a heat transfer process using one derived formula.