Since the chemical reactor is the heart of any chemical processing plant, there exist significant opportunities to increase industrial profits and minimize ecological impacts. One such opportunity is improving thermal stability in packed bed reverse-flow reactors. A fundamental study of the effect of multiscale, transient, thermal dispersion within packed bed reactors is undertaken here to evaluate its utility to improve thermal stability and satisfy economic and environmental goals. A new reactor configuration is investigated, where a regular pattern of cylindrical rods is inserted into the packed bed using a multiscale approach. These rods can increase the effective thermal dispersivity in the bed over thermal conduction by up to 2-orders of magnitude. It is found that the magnitude of the dispersion can be tuned by adjusting the key operating parameter, the reversal time, such that the reactor can stay ignited without the need for external fuel supply during extended lean conditions while remaining thermally stable during extended rich conditions. The ensuing multiscale thermal dispersion, in concert with a simple control strategy, allows for indefinite reactor operation without runaway or extinction, as predicted by simple, generalized analytical models for any chemical reaction and illustrated with numerical simulations. Some added benefits of this study are that the tight controllability of these reactors may allow for increased reaction selectivity, energy efficiency, and reduced pollution levels.