This paper presents an analytical solution for heating a rectangular sensible heat storage packed bed with a constant temperature at the walls by a non-thermal equilibrium how of incompressible fluid. A two energy equation model is employed to simulate the temperature difference between the fluid and solid phases. Using the perturbation technique, an analytical solution for the problem is obtained. It is shown that the temperature difference between the fluid and solid phases consists of the steady and transient components. The steady component is localized near the inlet boundary. The transient component describes a wave propagating from the fluid inlet boundary. The amplitude of the wave quickly decreases while the wave propagates downstream.