A common configuration of a catalytic packed-bed reactor is that of vertical downflow in which the fluid is distributed uniformly at the top of the reactor and reacts on the catalyst particles as it moves down. When an exothermic reaction occurs in this type of reactor, the physical properties of the fluid such as density and viscosity can vary significantly and induce natural convection which can destabilize the uniform down-flow. This leads to maldistributed flows and the formation of localized hot spots. In this work, we present a method for determining the critical residence time at which the one-dimensional down-flow in a packed-bed reactor becomes unstable.