A numerical study is made to investigate the forced laminar convection in the hydrodynamically and thermally fully developed region of a curved isothermal square duct. Solutions with one and two pairs of vortices superimposed on the main flow are obtained. In the thermally fully developed region, a three-dimensional energy equation of elliptic type is reduced to a two-dimensional one with an eigenvalue, and the axial diffusion term is considered for a small value of the Peclet number. Flow characteristics for cases of dimensionless radius of curvature β = ∞, 50, 10, and 5 with the square of the Dean number ranging from 0 to 106 in a square duct are studied. In addition, heat transfer characteristics for large dimensionless radii of curvature, Pr=0.7 and 7.0, and Peclet number Pe=∞, 10, 5, and 1 are also examined.