Measurements of the mass/heat transfer coefficients on the blade and end wall surfaces of a linear turbine cascade are compared to numerical predictions using the standard shear stress transport (SST) closure and the SST model in combination with the Reθ–γ transition model (SST-TRANS). Experiments were carried out in a wind tunnel test section composed of five large-scale turbine blades, using the naphthalene sublimation technique. Two cases were tested, with exit Reynolds number of 600,000 and inlet turbulence values of 0.2% and 4%, respectively. The main secondary flow features, consisting of the horseshoe vortex system, the passage vortex, and the corner vortices, are identified and their influence on heat/mass transfer is analyzed. Numerical simulations were carried out to match the conditions of the experiments. Results show that large improvements are obtained with the introduction of the Reθ–γ transition model. In particular, excellent agreement with the experiments is found, for the whole spanwise extension of the blade, on the pressure surface. On the suction surface, performance is very good in the highly three-dimensional region close to the end wall, but some weaknesses appear in predicting the location of transition in the two-dimensional region. On the end wall surface, the SST model in combination with the transition model produces satisfactory results, greatly improved compared to the standard SST model.