A boundary-layer model for a plane free-burning high-pressure gas-discharge arc is given. For the dependence on the temperature, a rule given by Elenbaas [The High Pressure Mercury Vapour Discharge (North-Holland, Amsterdam, 1951)]is used for the electrical conductivity and power-law rules for the dynamic viscosity and the thermal conductivity. The specific heat is assumed to be constant. It is shown that a similarity transformation can be applied. The upward velocity increases with the square root of the core temperature. Graphs are given which show how the temperature rise in the arc depends upon the applied current.