During sintering two solids bond together and reduce the total surface to minimize their interfacial energy. It is an important phenomenon in many processes, including 3D printing, where the sintering of 3D printed layers conditions strongly the mechanical properties of 3D printed parts. Heat transfer can have a strong effect on the sintering dynamics. In amorphous materials, the viscous dissipation is increased at lower temperature, due to the higher viscosity, thus slowing down the sintering dynamics. Numerical simulations of sintering consider fluid inertia and result in a slower dynamics than the simplified analytical models often used in the literature. However, up to now, even the numerical simulations have neglected the strong viscosity gradients that can result from temperature gradients and have instead considered an uniform effective viscosity. We present a novel and generic approach to simulate the sintering coupled with heat transfer, able to consider layers with circular or elliptical cross sections and materials with a strong dependency of viscosity with temperature. We apply this approach to the sintering and cooling of two 3D printed food layers and quantify the strong viscosity gradients occurring within the sintering layers as a result of the heat transfer. The effect on the sintering and cooling dynamics of printing process parameters such as the layer size, external and nozzle temperatures and heat transfer coefficient has been investigated. Lowering the layer thickness enhances both the sintering and the cooling dynamics; whereas lower nozzle temperature slows down the sintering process due to the lower initial viscosity. The results presented in this study can help optimising 3D printing conditions or material formulation. The novel simulation approach presented can be applied to a wide range of other sintering processes where viscosity gradients cannot be neglected.