In the next few years the electrical power embedded in future aircrafts will strongly increase. The supply voltage will increase to 230 VAC and ± 270 VDC or 540 VDC; thereby studies concerning the embedded equipment behavior must be done. For such power networks characteristics the risk of arc fault and requirements for arc tracking will also increase. The aim of this work is to propose a simple 1D model of a DC short gap electric arc in aeronautical pressure conditions: i.e. a pressure in the range [10 mbar-1 bar] which corresponds to the aircrafts altitudes. By emitting certain assumptions, the approach is to find the temperature distribution in the arc column and deduce from that the characteristics of the arc current as a function of electric field in the column and the maximum temperature in the center of the arc column. The novelty of this work is the observation of the evolution of the temperature (and as a consequence the evolution of the arc current) if we assume that the radius of the arc column is not limited like in wall stabilized arc where the wall is water cooled, the arc radius can expand as much as possible. The study is done in the air.