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 taken tolerance into consideration by using the analysis results. Response surface method is employed as an optimization technique. The objective function is defined as a combination of heat transfer rate and inverse of pressure drop. 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.