We report on large-eddy simulations (LES) of the effects of system rotation on heat transfer in a fully-developed flow in an asymmetrically-ribbed rectangular duct at Re=[Formula presented]=15000 where D_h is the hydraulic diameter and U₀ the bulk flow velocity. The bottom duct wall, ribbed by flow-normal, equally-distanced square-sectioned ribs, was uniformly heated (except for the ribs) with an imposed constant heat flux. The duct was rotated with a spanwise angular velocity Ω corresponding to two rotation number Ro=[Formula presented]=±0.3, destabilising and stabilising respectively the ribbed-wall adjacent flow. The computational method and the treatment of heat transfer were verified and validated in prior simulations of generic well-documented reference configurations, rotating plane channel and non-ribbed duct flows. The well-resolved LES gave some new insight into the rotation effects on flow and heat transfer, providing information that are not easily accessible to experiments. An attempt is made to identify and distinguish the physical mechanisms of heat transfer enhancement and suppression by system rotation, rib-induced modifications of secondary motion, and the direct effects on the turbulence statistics, especially on the budgets of the turbulent kinetic energy, temperature variance and turbulent heat flux components.