The first observation of the Ne III 36.02 micron forbidden line in a planetary nebula, NGC 6543, is presented. Since the dominant form of neon in medium-excitation to high-excitation planetary nebulae is Ne III, the abundance of this ion is important in determining the total neon abundance. Use of the 36 micron line for an abundance determination has the advantage of insensitivity to temperature uncertainties. However, current atomic parameters lead to a Ne III abundance in NGC 6543 which is 4.5 times the cosmic neon abundance and 2.6 times the abundance from optical line studies. Although such a high abundance cannot be ruled out immediately, inaccuracies in the infrared level collision strengths are suspected because resonances were neglected in their calculation. The 36 micron line is also useful as a temperature probe when combined with the Ne III 3868-A forbidden line. When compared to Ne III 15.56 micron forbidden line fluxes, a temperature-insensitive density estimate may be obtained. The utility of these line ratios depends upon the actual infrared level collision strengths, which will affect the density range over which they are sensitive.