A variety of biochemical reactions involve cycling reagents through different temperature regimes in a specific order as dictated by chemical kinetics. One such reaction is the polymerase chain reaction (PCR), a fundamental process used to selectively amplify specific regions of interest within a larger DNA strand to very high concentration levels. Natural convection has recently been explored as a novel way to perform PCR by providing a passive approach to circulate reactants through the correct temperature zones. Optimal reactor design requires the spatial velocity and temperature distributions to be precisely controlled to ensure that the reactants sequentially occupy the correct temperature zones for a sufficient period of time. Rayleigh-Benard convection in vertical cylindrical reaction chambers maintained at fixed upper and lower surface temperatures provides a convenient model system to study these phenomena. In this work, we present results of three dimensional numerical simulations of the flow and temperature distributions in cylindrical reactors of different aspect ratios (height (h) / diameter (d)). These results helped identify different flow profiles that are possible in each of the geometries and led to an optimized redesign of the Rayleigh-Benard PCR convection system for rapid DNA replication.