A mathematical model that depicts thermally enhanced facilitated transport (TEFT) is developed under the combined framework of liquid-liquid extraction (LLX) and facilitated transport (FT). Assuming negligible mutual miscibility between the solute and the solvent, an analytical solution is presented with simulations of TEFT of citric acid by a tertiary amine. Under similar guidelines, an equivalent mathematical model is developed to describe the effect of temperature on FT for isothermal conditions. Simulations of this model are compared with experimental data of facilitated transport of citric acid on a supported liquid membrane (SLM). Simulations confirm the existence of an optimal operating temperature that coincides with that obtained experimentally, without the need of any parameter fitting. The effects of boundary conditions are also compared with experimental results, and the fit between the two is promising.