Direct numerical simulations of thermal convection over grooved plates are presented and discussed, in comparison with the standard flat-plate case, in order to gain a better understanding of the altered near-wall dynamics and of the enhancement of the heat transfer. The simulations are performed in a cylindrical cell of aspect-ratio (diameter over cell height) Γ = 1/2 at fixed Prandtl number Pr = 0.7 with the Rayleigh number Ra ranging from 2 × 106 to 2 × 1011. The results show an increase of heat transfer, or in non-dimensional form the Nusselt number Nu when the mean thermal boundary-layer thickness becomes smaller than the groove height, in agreement with earlier experimental investigations available from the literature. The present increase, however, results in a steeper power law of the Nu vs. Ra law rather than a simple upward shift of the Nu law of the flat plate. This finding agrees with some studies, but it is at variance with others. Possible causes for this difference are discussed with the help of an electrical analogy.