Large-eddy simulations of a compressible turbulent square duct flow at low Mach number are described. First, we consider the isothermal case with all the walls at the same temperature: good agreement with previous incompressible DNS and LES results is obtained both for the statistical quantities and for the turbulent structures. A heated duct with a higher temperature prescribed at one wall is then considered and the intensity of the heating is varied widely. The increase of the viscosity with temperature in the vicinity of the heated wall turns out to play a major rôle. We observe an amplification of the near-wall secondary flows, a decrease of the turbulent fluctuations in the near-wall region and, conversely, their enhancement in the outer wall region. The increase of the viscous thickness with heating implies a significant augmentation of the size of the characteristic flow structures such as the low- and high-speed streaks, the ejections and the quasi-longitudinal vorticity structures. For strong enough heating, the size limitation imposed by the lateral walls leads to a single low-speed streak located near the duct central plane surrounded by two high-speed streaks on both sides. Violent ejections of slow and hot fluid from the heated wall are observed, linked with the central low-speed streak. A selective statistical sampling of the most violent ejection events reveals that the entrainment of cold fluid, originated from the duct core, at the base of the ejection and its subsequent expansion amplifies the ejection intensity.