The flow of a rarefied gas in a square enclosure with one wall at high temperature and the other three walls at the same low temperature is investigated. The flow, characterized by the reference Knudsen number and ratio of the cold over the hot temperatures, is simulated both deterministically, using the nonlinear Shakhov kinetic model, and stochastically, using the DSMC method. Excellent agreement between the two approaches is obtained. It is found that along the side walls the gas velocity, depending on the flow parameters, may be either from cold to hot or from hot to cold regions. Furthermore, it is confirmed that the average heat flux departing from the hot plate exhibits a nonmonotonic behavior with regard to the temperature ratio, deducing a maximum heat flux at a temperature ratio of about 0.3. The flow and heat transfer characteristics are explained by computing the ballistic and collision parts of the total bulk quantities and by investigating the contribution of each part to the overall solution.