Abstract We carry out direct numerical simulations of turbulent Rayleigh–Bénard convection in a square box with rough conducting plates over the Rayleigh number range $10^7\leqslant Ra\leqslant 10^9$ and the Prandtl number range $0.01\leqslant Pr\leqslant 100$ . In Zhang et al. ( J. Fluid Mech. , vol. 836, 2018, R2), it was reported that while the measured Nusselt number $Nu$ is enhanced at large roughness height $h$ , the global heat transport is reduced at small $h$ . The division between the two regimes yields a critical roughness height $h_c$ , and we now focus on the effects of the Prandtl number ( $Pr$ ) on $h_c$ . Based on the variations of $h_c$ , we identify three regimes for $h_c(Pr)$ . For low $Pr$ , thermal boundary layers become thinner with increasing $Pr$ . This makes the boundary layers easier to be disrupted by rough elements, leading to the decrease of $h_c$ with increasing $Pr$ . For moderate $Pr$ , the corner-flow rolls become much more pronounced and suppress the global heat transport via the competition between the corner-flow rolls and the large-scale circulation (LSC). As a consequence, $h_c$ increases with increasing $Pr$ due to the intensification of the corner–LSC competition. For high $Pr$ , the convective flow transitions to the plume-controlled regime. As the rough elements trigger much stronger and more frequent plume emissions, $h_c$ again decreases with increasing $Pr$ .