An example of a nonequilibrium ensemble is constructed, a Knudsen gas in a container whose walls are maintained at different temperatures. The approach to a stationary state is investigated, and an iteration procedure for finding the stationary velocity distribution is derived. An explicit stationary solution is found for the case where a Knudsen accommodation coefficient completely characterizes the effect of gas collisions with the walls. The heat transport is found. A stochastic mathematical model which mimics in certain aspects the above system is investigated.