Rapid compression machines (RCMs) are widely used by the fuel research community to provide engine-relevant conditions to study ignition delay time (IDT), which is a crucial target for validating chemical kinetic mechanisms for fuels. Creviced piston heads are routinely used to ensure temperature homogeneity within the combustion chambers of RCMs. However, due to the exponential dependence of kinetic rate coefficients on temperature, homogeneity of the temperature field is vital for a clear interpretation of results and identification of chemical kinetic mechanisms. The overall aims of this work are to (1) support operators of RCMs in ensuring that their devices achieve sufficient levels of in-chamber temperature homogeneity and (2) validate performance of a previously-developed correlation for temperature inhomogeneity in RCMs at different conditions. Large Eddy Simulation (LES) is conducted to resolve 3D unsteady structure of turbulent flow, throughout compression and long post-compression times, at two representative operating conditions in the NUI Galway RCM. Results show that at higher pressures, 3D LES temperature and velocity fields are well approximated by a previous 2D laminar model. At low pressures, 2D laminar and 3D LES agree well for flow during compression, but predict different evolution of roll-up vortices and temperature distribution after compression. However, across all conditions there is a satisfactory agreement between 2D laminar and 3D LES results for global temperature inhomogeneity. Moreover, the previously developed correlation (based on 2D laminar simulations) for temperature inhomogeneity is found to agree with 3D LES to within +/- 20%. Therefore, the correlation may be used for preliminary design and evaluation of RCMs and RCM experiments. We propose a framework for design of RCM experiments based on the use of correlations, supported by 2D laminar simulations, and finally 3D LES of selected cases for confirmation.