The plane, steady, laminar vortex flow of a viscous, heat-conducting perfect gas is treated. Simple relations are obtained for the flow quantities in the irrotational vortex, for arbitrary Prandtl numbers. When the Prandtl number is ½, the irrotational vortex is also isentropic. When the temperature dependence of the viscosity coefficient is taken into account, the vortex flow is rotational. An exact solution for the rotational vortex is obtained which is suitable for numerical evaluation by successive approximations. Distributions of velocity, temperature, pressure, density, and stagnation temperature through the rotational vortex are given for a typical case.