Large-Eddy Simulations (LES) of the turbulent compress-ible flow within heated curved ducts of square cross section are presented. The aim here is to predict the three-dimensional structures which develop inside cooling channels of rocket engines and study their effect on heat transfer rates. In this work, we focus on the influence of the Reynolds number on these structures and thus on the heat transfer characteristics. We first consider non heated curved ducts for two Reynolds numbers : 6000 and 12000. We observe that the the Ekman vortices corresponding to the secondary flow created by the radial pressure gradient become larger in size at high Reynolds number. The Görtler vortices appearing on the concave wall, due to the centrifugal instability, are conversely smaller and more numerous. We then present simulations with heat: a constant heat flux is imposed on the convex wall of the curved duct. The Ekman vortices are found to be associated with an important transverse temperature gradient on the heated wall. This gradient intensifies when the Reynolds number is increased.