The non-orthogonal boundary-fitted coordinate transformation method is applied to the solution of steady three-dimensional momentum and energy equations in laminar flow to obtain temperature field and Nusselt numbers in the thermal entry region of straight ducts of different cross sectional geometries. The conservation equations originally written in Cartesian coordinates are parabolized in the axial direction and then transformed to the non-orthogonal curvilinear coordinate system to handle arbitrary duct geometries. The transformed equations are discretized using the control-volume finite-difference approach in which the convective and diffusive terms are discretized by the upwind and central difference schemes respectively. The discretization equations are solved by a line-by-line TDMA algorithm. Numerical results of Nusselt numbers and temperature profiles are obtained for constant wall temperature boundary condition and Pr = 6.78.