  A laser can be understood as thermodynamic engine converting heat to a
coherent single mode field close to Carnot efficiency. From this perspective
spectral shaping of the excitation light generates 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 temperature, we study a laser operated on an actual spatial
temperature gradient between pump and gain region. We predict gain and narrow
band laser emission for a sufficient temperature gradient and resonator
quality. Lasing appears concurrent with amplified heat flow and points to a new
form of stimulated solid state cooling. Such a mechanism could raise the
operating temperature limit of quantum cascade lasers by substituting phonon
emission driven injection, which generates intrinsic heat, by an extended model
with phonon absorption steps.
