Conjugate heat transfer (CHT) computational fluid dynamic (CFD) predictions were carried out for a 10 × 10 square array of impingement holes, for a range of pitch to diameter ratio X/D from 1.9 to 11.0 at a constant impingement gap Z of 10 mm and pitch X of 15.24 mm. The variation of X/D changes the impingement wall pressure loss for the same coolant mass flow rate and also changes the interaction with the impingement gap cross-flow. The experimental technique to determine the surface averaged heat transfer used the lumped capacity method with Nimonic-75 metal walls with imbedded thermocouples and a step change in the hot wall cooling to determine the heat transfer coefficient h from the transient cooling of the metal wall. The test wall was electrically heated to about 80 °C and then transiently cooled by the impingement flow and the lumped capacitance method was used to measure the locally surface average heat transfer coefficient. The predictions and measurements were carried out at an impingement jet mass flux of 1.93 kg/s m2 bar, which is a typical coolant flow rate for regenerative impingement cooling of low NOx gas turbine combustor walls. The computations were conducted for a fixed hot side temperature of 353 K that was imposed at the hot face of the target wall. The wall temperatures as a function of distance along the gap were computed together with the impingement gap aerodynamics. Surface average heat transfer coefficient h and pressure loss predictions were in good agreement with the experimental measurements. However, there was less good agreement for the axial variation of the local surface averaged h for lower values of X/D. The surface averaged heat transfer to the impingement jet wall was also computed and shown to be roughly 70% of target wall impingement heat transfer.