The interest for hydrogen-fuelled combustors is recently growing thanks to the development of gas turbines fed by high content hydrogen syngas. The diffusion flame combustion is a well-known and consolidated technology in the field of industrial gas turbine applications. However, few CFD analyses on commercial medium size heavy duty gas turbine fuelled with pure hydrogen are available in the literature. This paper presents a CFD simulation of the air-hydrogen reacting flow inside a diffusion flame combustor of a single shaft gas turbine. The 3D geometrical model extends from the compressor discharge to the gas turbine inlet (both liner and air plenum are included). A coarse grid and a very simplified reaction scheme are adopted to evaluate the capability of a rather basic model to predict the temperature field inside the combustor. The interest is focused on the liner wall temperatures and the turbine inlet temperature profile since they could affect the reliability of components designed for natural gas operation. Data of a full-scale experimental test are employed to validate the numerical results. The calculated thermal field is useful to explain the non-uniform distribution of the temperature measured at the turbine inlet.