  We present a numerical study of Rayleigh-B\'enard convection disturbed by a
longitudinal wind. Our results show that under the action of the wind, the
vertical heat flux through the cell initially decreases, due to the mechanism
of plumes-sweeping, and then increases again when turbulent forced convection
dominates over the buoyancy. As a result, the Nusselt number is a non-monotonic
function of the shear Reynolds number. We provide a simple model that captures
with good accuracy all the dynamical regimes observed. We expect that our
findings can lead the way to a more fundamental understanding of the of the
complex interplay between mean-wind and plumes ejection in the
Rayleigh-B\'enard phenomenology.
