An approximate method for solving the partial differential equation of conduction is developed that is continuous in time and discrete in space. The general solution is presented for a slab having five nodes and time dependent boundaries and having an arbitrary initial temperature distribution. The corresponding case, for a four node and a three node slab, is given in Appendix I. A typical example for a slab is solved using this quasi-analytic method, as well as by the traditional finite difference method. Both approximate solutions of the example problems are compared graphically with the exact solution.