The problem of transient temperature fields' estimation is formulated and resolved for the packed layer furnaces and heat exchangers with counter-current material and gas flow. When the gas temperature at entrance into the process unit and heating gas rate were considered as disturbances, an analytical solution was developed. The analysis of this solution and the results of numerical modeling showed that transient heat transfer processes in the packed bed units have a monotonous aperiodic character. The timing for the new steady state conditions establishment mainly depends on the type of disturbance, ratio of material and gas flow heat capacities and the availability of a heat source (heat sink).