A 3-dimensional, coupled, heat transfer model and solution for multi-hole cooling is described in this paper. It couples DNS calculations of the primary turbulent flow, the backside flow and the flow in the injection holes by solving the 3-D heat conduction equation for the wall with a mixed boundary condition, which leads to an iteration process to obtain a converged solution for the mean temperature in the wall and in the flow. The model is tested for both a laminar and a turbulent primary flow and the results show that the convergence to the solution is very efficient. The results obtained with this 3-D model are presented and compared with an adiabatic and a 1-D, conducting-wall, model. A non-dimensional parameter (Biot number) representing the relative importance of in-plane heat conduction in the wall is discussed. The cooling effectiveness predicted by the 3-D model is compared with experimental results at the same Reynolds number and satisfactory agreement is achieved. (c) 2006 Elsevier Ltd. All rights reserved.