The purposes of present work are to analyze the convective heat transfer with three-dimensional Reynolds-averaged Navier-Stokes analysis, and to optimize shape of the mixing vane using the analysis results. Response surface method is employed as an optimization technique. The objective function is defined as a combination of inverse of heat transfer rate and friction loss. Two bend angles of mixing vane are selected as design variables. Thermal-hydraulic performances have been discussed and optimum shape has been obtained as a function of weighting factor in the objective function. The results show that the optimized geometry improves the heat transfer performance far downstream of the mixing vane.