We consider heat transport within a discontinuous domain by relying on the modeling approach proposed by Baioni et al. in part I of this paper. Such approach has been specifically designed to address diffusive processes in media with discontinuous physical properties and generalized boundary conditions at the discontinuities. Three algorithms are here applied to estimate the conductive heat transport in a bimaterial medium. The algorithms undergo testing using two test cases that share the same computational domain but differ in terms of their initial conditions. According to the numerical results all the algorithms ensure the conservation of thermal energy and preserve thermal equilibrium under steady state conditions. The Generalized Uffink Method (GUM) and Generalized HYMLA (GHYMLA) demonstrate sensitivity to the choice of the time step, whereas the Generalized Skew Brownian Motion (GSBM) appears to be unaffected by the value of ∆t. The GUM algorithm presents an optimal trade-off between accuracy and computational time.