We apply several physical ideas to determine the steady temperature distribution in a medium moving with uniform velocity between two infinite parallel plates. We compute it in the coordinate frame moving with the medium by integration over the "past" to account for the influence of an infinite set of instantaneous point sources of heat in past moments as seen by an observer moving with the medium. The boundary heat flux is simulated by appropriately distributed point heat sources on the inner side of an adiabatically insulating boundary. We make an extensive use of the Green functions with an emphasis on their physical meaning. The methodology used in this paper is of great pedagogical value as it offers an opportunity for students to see the connection between powerful mathematical techniques and their physical interpretation in an intuitively clear physical problem. We suggest several problems and a challenging project that can be easily incorporated in undergraduate or graduate courses. (Contains 2 figures.)