Heat transfer control is crucial for flow assurance in transport as well as production operations of oil and its derivatives in subsea lines. If the product temperature falls below certain critical values, problems such as hydrate formation or wax deposition in the pipelines walls can occur, inducing line blockage and interruption of production, demanding high costs. The heat loss to the environment is minimized by employing thermal insulation, which are designed for stead state operations. For these cases, due to high axial velocities, the flow is typically turbulent, and the dominant heat transfer mechanism is due to convection forced. However, during maintenance operation of some equipment, the production can be interrupted and the stagnant fluid in the interior of the line tends to cool down and it can reach a critical temperature. During this cooling, in the absence of pumps, the process of natural convection begins to dominate. The present work analyzes the heat transfer process after flow shutdown, considering the effect of the natural convection, as well as the influence in the thermal transient of the thermal capacity of the duct wall and insulation layers. Initially, it is considered that the axial flow is set to rest very quickly and a two-dimensional model of the transversal section of the duct is employed, using three typical products: light oil, heavy oil and pressurized gas. The velocity and temperature filed are obtained using the numerical software FLUENT, considering the hypothesis of Boussinesq to evaluate the natural convection. The cooling rate is compared with the forecast of a unidimensional model in the axial direction based on empirical correlations, function of the flow regime, to evaluate the heat transfer between the fluid and the duct wall. Good agreement is obtained between the solutions of the 2-D model and the pipeline central cross section of the 1-D model. However, as the axial variations for the gas case are significant, for this product, a three-dimensional model also was analyzed, where it was considered the effects of the forced and natural convection. Additionally, the hypothesis of Boussinesq was eliminated, and the ideal gas equation was considered.