  Contemporary models of bounded plasmas assume that the target plasma electron
temperature far exceeds the temperature of the cold electrons emitted from the
target, T_emit. We show that when the sheath facing a collisional plasma
becomes inverted, the target plasma electron temperature has to equal T_emit
even if the upstream plasma is hotter by orders of magnitude. This extreme
cooling effect can alter the plasma properties and the heat transmission to
thermionically emitting surfaces in many applications. It also opens a
possibility of using thermionic divertor plates to induce detachment in
tokamaks.
