We consider a periodic bounded horizon dispersing billiard table with scatterers acting as thermostats set at possibly different temperatures. That is, whenever a particle with velocity v hits a thermostat, the tangential component vt of the particles velocity is instantaneously set to a random value sampled from the distribution with density qβπe−βvt, where T = 1/β represents the thermostat temperature; the perpendicular component of the velocity changes sign. The particles do not interact with each other. For certain classes of such systems, we will discuss existence, uniqueness, and ergodic properties of the stationary measures.