We extend the formulation of the stages/substages model described in the first part of this series to account for variable heat capacity with temperature, whose influence on heat exchanger network design was not studied. Variable heat capacity (Cp) frequently arises when streams of high molecular weight are used, or when temperature ranges are large, such as in petroleum fractionation, where the range of temperatures in streams spans more than 100 degrees C. We solve our model globally using RYSIA, a recently developed method bound contraction procedure (Comput. Chem. Eng. 2011, 3S, 446-455; Ind. Eng. Chem. Res. 2015, 54 (5), 1595-1604). We also tried BARON and ANTIGONE, two commercial global solvers, but they failed to find a solution.