This paper considers the heat transfer in a vertical rectangular duct filled with Newtonian fluid. The viscosity of the fluid is assumed to depend on the temperature. The governing fundamental equations are approximated by a system of nonlinear ordinary differential equations and are solved numerically by using the finite difference method. The steady-state velocity and temperature contours are shown graphically. Numerical results for the skin friction, volumetric flow rate and the rate of heat transfer are obtained and reported in a tabular form for various parametric conditions to show interesting aspects of the solution. The results show that the negative values of viscosity variation parameter show intense velocity contour in the lower half region of the duct whereas positive values of viscosity variation parameter show the intense velocity contours in the upper half region of the duct. The temperature contours remain almost linear for any variations of governing parameters for all values of viscosity variation parameter. (C) 2015 Elsevier Ltd. All rights reserved.