This paper presents a generally applicable approach to numerical thermal design. A novel thermal design procedure for the prediction of heat transfer inside a pressure vessel of an ocean current turbine using integrated procedure by finite element method of heat transfer analysis, artificial neural network and genetic algorithms is presented. Numerical heat transfer analysis was done using commercial software ANSYS for two-dimensional heat transfer in simplified domains. The calculation was limited to only heat conduction. The ANSYS simulations results were used for training and approximating the unknown functional behaviour of heat transfer by using artificial neural networks (ANN). The trained ANN serves as the nonlinear objective function of the optimisation procedure. Genetic algorithms (GA) were used as the optimisation tool. The optimum results obtained from the GA were verified against ANSYS and ANN results. Both the ANN and GA were implemented in MATLAB, while the overall methodology proposed could be applied to other engineering design problems as well.