The problem of two-dimensional steady flow of an incompressible second-order viscoelastic fluid coupled with heat transfer between parallel plates was considered.A viscous dissipation function was included in the energy equation.When the elastic property of the fluid is weaker, the zeroth-order and first-order approximate governing equations were obtained by means of the perturbation method.To understand the behavior of flow near the tube wall, the half-domain was divided into two sub-domains, in which one is a thin layer near the wall called the inner domain and the remainder is called the outer domain.The governing equations in the inner domain and in the outer domain were discretized respectively by using the Differential Quadrature Method (DQM).The matching conditions at the interface between the inner and outer domains were presented.An iterative method for solving these discretized equations was given in this paper.The numerical results obtained agree with existing results.