We developed a decimetric size model based on coupling generalized Darcy's law and heat-transfer equations to model viscous dense non-aqueous phase liquid (DNAPL) pumping through highly permeable porous media under non-isothermal conditions. The presence of fingering and non-wetting phase ganglia was modeled through an unsteady capillary diffusion coefficient and an arbitrary heterogeneous permeability field. The model was validated using existing experimental data of a simple case, an oil injection in a 2D tank packed with glass beads. Next, we compared the results of this model against a DNAPL extracting situation in the 2D tank to better understand the two-phase flow behavior in highly permeable porous media. We found that natural convection during heating plays an essential role in heat transfer, especially in the wetting phase zone. By adding the dynamic effect (unsteady conditions) we were better able to describe the presence of the ganglia in porous media. We observed good agreement between modeled and experimental oil saturation curves until the breakthrough point, with a mean relative error of about 10% for low and high flow rates, and 8% and 16% after breakthrough for low and high flow rates, respectively. Extracting viscous oil at low flow rates and high temperature generates less fingering and is well described by the generalized Darcy's law. The remobilization of residual non-wetting ganglia after the breakthrough point at the outlet is, however, difficult to simulate using the generalized Darcy's law. In the end, we treated this issue by using a perturbed permeability field to simulate the observed fingering in the 2D tank.