An easily implemented, finite-difference predictor-corrector numerical technique originated by MacCormack is used to solve for fluid and solid temperature distributions in one-dimensional flow through a finite packed bed. The method allows for temperature dependent properties, time-varying inlet conditions and nonuniform initial conditions. The numerical method agrees with the classical Schumann model to within 1% in simulations which exhibit fully-developed thermal gradients of 310/sup 0/C/m. Additional examples demonstrate the flexibility of the technique and that the constant property assumption may lead to temperature distributions significantly different from a more realistic variable property assumption. The attractiveness and uniqueness of the method is, then, its accuracy, flexibility, ease of implementation and efficiency computation-wise.