In this research, with regards to the considered geometrical parameters, a multi-objective optimization has been performed with the goal of achieving maximum heat transfer and minimum pressure loss in a swirl chamber. This objective has been accomplished by using the Computational Fluid Dynamics (CFD) technique, GMDH type Neural Network and the NSGA-II multi-objective optimization algorithm. The design variables include the ratio of inlet slot width to swirl chamber diameter, ratio of inlet slot height to swirl chamber diameter and the inlet slot angle. These variables are just related to geometrical parameters; and the Reynolds number, tangential jet temperature and the wall temperature are considered as constant. The objective functions include the averaged Nusselt number over swirl chamber wall and the pressure loss coefficient. CFD technique is used to analyze the flow and heat transfer and to compute the values of objective functions. The polynomials that relate the objective functions to input variables are obtained by means of GMDH algorithm. The obtained models are used to predict the values of objective functions as inputs for NSGA-II multi-objective optimization. Considering the range of changes of design variables, Pareto optimal points are obtained for the objective functions, and the Pareto points with special characteristics are introduced and discussed.