The flow of air and fuel in internal combustion engine cylinders is almost always turbulent. The more turbulent the air flow is, the greater the degree of mixing air and fuel that can be achieved prior to ignition. Although turbulence at the instant of ignition may lead to rapid and complete combustion, it is also related to higher rates of heat transfer to the cylinder walls that reduce the engine's thermal efficiency. Within the MINNOX project, some of the major names in the European automotive industry joined their experience and expertise with Europe's leading universities. Their ultimate aim was to develop a physical model for accurate predictions of heat transfer, velocity and temperature profile inside the cylinder of an internal combustion engine. This model would be validated with measurements provided by an advanced experimental setup developed during the course of the project. The numerical approach is particularly attractive for the automotive industry due to its ability to produce and analyse results within a reasonable time frame. It can introduce a significant speed-up in the engineering design and furthermore, in its optimisation process. The model proposed by project partners at the Delft University of Technology is simple so that it can be implemented into commercial Computational fluid dynamics (CFD) codes. Yet, it is able to capture the most important effects occurring in the engine cylinder, including near wall and transient effects. The approach adopted in this work was elliptic relaxation modelling, which is one step ahead of the current two-equation models but still one step behind the full Reynolds stress model. For a turbulence model requiring sufficiently fine computational meshes, new generalised wall functions that are not constrained by the common equilibrium assumptions were added. Verification of the model in idealised configurations was shown to be in agreement with temperature and velocity calculations from experimental and large-eddy simulation (LES) data.