A laser can be understood as a thermodynamic engine converting heat to a coherent single mode field close to Carnot efficiency. To achieve lasing, spectral shaping of the excitation light is used to generate a higher effective temperature on the pump than on the gain transition. Here, using a toy model of a quantum well structure with two suitably designed tunnel-coupled wells kept at different temperatures, we predict that lasing can also occur on an actual spatial temperature gradient between the pump and gain regions. Gain and narrow band laser emission require a sufficiently large temperature gradient and resonator quality. Lasing appears concurrent with amplified heat flow between the reservoirs and points to a new form of stimulated solid state cooling. In addition, such a mechanism could reduce intrinsic heating and thus extend the operating regime of quantum cascade lasers by substituting phonon emission driven injection by a phonon absorption step.