[en] The case of a pulse of high intensity electromagnetic radiation of nuclear origin with a thermal flux level of the order of 10⁷ watts/cm² or greater may generate the surface temperature and its gradient significantly greater than the classical models. Plasma torch is another example for presence of large heat fluxes. Classical steady and unsteady heat conduction problems are well known. All these problems can be special cases of a more generalized heat diffusion model where first and second order derivatives in both two-dimensional space and time appear. The generalized equation may be hyperbolic (large heat fluxes), elliptic (independent of time), or parabolic (classical Fourier) depending upon the parameters chosen. Since the mathematical characteristics are different for each, it is common to utilize specialized techniques for each class of problems. Recently Yalamanchili showed that the finite-element and finite-difference belong to the class of method of weighted-residuals and pointed out that the finite-element method is inferior to some other possible variations of finite-difference method in accuracy and nonoscillation characteristics. Therefore, the explicit finite-difference scheme is utilized for the generalized transient two-dimensional diffusion equation. A transient one-dimensional example with step change in temperature on one side and insulated on the other surfaces is computed