Abstarct: Flow of non-Newtonian fluids in straight non-circular ducts is one of the interesting subjects for researchers since 1950, because they are often required for a wide range of industrial applications. So far, extensive researches with numerical, analytical and experimental methods with viscoelastic fluids in different geometries and using different models have been done. In some of them, just the flow equations have been solved but in others, the energy equation has been considered too. In these researches, which have done with various methods and geometries, heat transfer is in developing state, but in most of them, the flow has been assumed in the fully developed zone. Therefore, the effects of inlet region of fluid flow and heat transfer are neglected. The current study presents a 3D numerical simulation of the developing flow and heat transfer of a viscoelastic fluid in a rectangular duct. In fully developed flow of a viscoelastic fluid in a non-circular duct, secondary flows normal to the flow direction are expected to enhance the rate of heat and mass transfer. On the other hand, some properties such as viscosity, thermal conductivity, specific heat and relaxation time of the fluid are a function of temperature. Therefore, we developed a numerical model which solves the flow and energy equations simultaneously in three dimensional form. We included several equations of state to model the temperature dependence of the fluid parameters. The current study is one of the first studies which present a 3D numerical simulation for developing viscoelastic duct flow that takes the dependency of flow parameters to the temperature into account. The rheological constitutive equation of the fluid is a common form of the Phan-Thien Tanner (PTT) model, which embodies both influences of elasticity and shear thinning in viscosity. The governing equations are formulated explicitly by applying the artificial compressibility method and first-order forward finite difference in time and second-order central finite difference (FTCS) are used for discretization in space. The solution domain was latticed by a staggered mesh as primary and secondary grids and the marker-and-cell method is used to allocate flow variables on the staggered mesh. Considering the pressure which is defined on the internal grids and the boundaries which are located on the external grids and also absence of the second order derivatives of pressure, the discretization can be done in a manner that does not need to define a boundary condition for pressure. It should be noted that, the original form of the momentum equation was elliptic. With applying the artificial compressibility method, these equations will turn to the parabolic form. In this case, it is necessary to define the initial conditions. Hence, the initial velocity in transverse directions is assumed to be zero and the initial velocity in axial direction and also initial temperature assumed to be one. The initial values for other temperature dependent properties are assumed to be equal to their value at the inlet temperature. Therefore, after choosing a suitable initial condition, the equations are solved in time until converging to a steady state solution. On the solid boundaries (walls) no slip condition is applied for velocity and a constant heat flux and also constant temperature are imposed for the temperature. Other boundary conditions at the symmetry boundaries are applied according to mirrored property. On channel input, the axial uniform velocity and temperature profiles and on the output of the channel fully developed flow assumptions are considered. In the explicit method used in this study, after solving the governing equation with the initial value, the temperature dependent properties will be updated and the processing continue to achieve the steady state results. In addition to report the results of flow and heat transfer in the developing region, the effect of some dimensionless parameters on the flow and heat transfer has also been investigated. The results are in a good agreement with the results reported by others in this field.