The investigation of flows in non-circular ducts of various sectional shape is of considerable engineering interest. In this paper, we perform simulations of the turbulent compressible flow in a duct of square cross section with streamwise curvature. The aim is to predict, by Large Eddy Simulation (L.E.S), the three-dimensional structures which develop inside the cooling channels of rocket engines and which are responsible for most of the heat transfer with the heated wall. Three simulations are performed : the first one with the same temperature on the four walls, the others with a higher temperature on the concave wall or on the convex wall. For the curved duct configuration, a centrifugal instability appears on the concave wall generating two longitudinal vortices which move towards the convex wall further downstream. These simulations allow for the evaluation of the impact of these structures on the heat transfert and reciprocally.