As a temperature-sensitive non-Newtonian fluid, the seepage of heavy crude oil in porous media shows the non-linear characteristics. The flowing behavior of three heavy oils through porous media is experimentally investigated, and the influence of temperature and pressure-drop on this flowing process is also described. Thereafter, based on the flowing behavior of heavy crude oil, the new models of productivity of the thermal producers (including vertical well and horizontal well) are proposed. In these models, both the threshold pressure gradient (TPG) and thermal effect are taken into account. The flowing experiments of heavy oil in porous media indicate that the pressure gradient and temperature have the significant influence on the flowing process because of the existence of threshold temperature and TPG. Heavy crude oil begins to flow only when the pressure gradient is in excess of TPG, and there dose not actually exist TPG above the threshold temperature. The viscosity-temperature curves demonstrate that the viscosity of heavy crude oil has an obvious feature of two straight-lines on semilog coordinate. On account of the damage of overlapping phenomena of asphaltenes in crude oil, when temperature is higher than the critical temperature, the reducing trend of TPG (with the increase of temperature) will be lessened. Furthermore, on the basis of flowing process of heavy crude oil, the concepts of threshold temperature and certain production temperature of thermal wells are introduced. That heavy oil with a higher viscosity would have a higher threshold temperature, as well as the certain production temperature. The application of horizontal wells tremendously increases the oil recovery rate in comparison with the vertical wells. This investigation could be used as a tool to study the flowing process of heavy oil and productivity calculation of thermal wells in heavy oil reservoirs. © 2012 The Author(s).