The steady magnetohydrodynamics (MHD) laminar compressible flow of an electrically conducting fluid on a porous rotating disk is considered in the present paper. The governing equations of motion are reduced to a set of nonlinear differential equations by means of similarity transformations. The fluid properties are taken to be strong functions of temperature and Hall current that also readily accounts for the viscous dissipation and Joule heating terms. Employing a highly accurate spectral numerical integration scheme, the effects of viscosity, thermal conductivity, Hall current, magnetic field, suction/injection, viscous dissipation, and Joule heating on the considered flow are examined. The quantities of particular physical interest, such as the torque, the wall shear stresses, the vertical suction velocity, and the rate of heat transfer are calculated and discussed.