The aim of the present study is to characterize the ability of several common URANS and near-wall models to simulate the turbulent flow and heat transfer around heated bluff bodies. Standard, RNG and realizable k-epsilon models and standard and SST k-omega models are tested. We chose the ERCOFTAC benchmark proposed by Rodi et al. [JFM, 1995] of a flow around a square cylinder, placed transversally at mid-height of a channel, at Re=22,000, but considering that the cylinder is heated. A detailed experimental and numerical (LES) database of the flow dynamic is available with also a thermal database thanks to the experiments by Igarashi [IJHMT, 1986] and Yoo et al. [JHT, 2003]. The objectives of this work are (i) to establish a reference solution for the chosen test case from the experimental results of literature, (ii) to identify the most accurate combination of URANS and near-wall models usually used in industry by comparing the URANS solutions with the reference solution and, (iii) to identify the coarser grid sizes allowing enough accurate solutions at low computational cost. The analyzed quantities are local and global quantities such as mean and rms velocity and temperature profiles, the profiles of the time averaged friction coefficient and Nusselt number around the square cylinder, the Strouhal number, etc. The ability to simulate the flow dynamic of Rodi’s benchmark has already been tested with various URANS and LES models. On the other hand, to our best knowledge, the ability to simulate the heat transfer around a single square cylinder has been tested with LES but not with URANS models. The k-omega SST model is shown to provide the most accurate results both for the flow dynamics and heat transfer.