We report first detections of the [Na IV] 9.04-mu-m and the [Ar V] 13.09-mu-m fine-structure emission lines, observed in the well-studied planetary nebula NGC 7027. The Na IV 9.04-mu-m/3242 angstrom line ratio is shown to be an excellent temperature diagnostic for highly ionized regions. With the addition of the Ne v 24.32-mu-m/3426 angstrom line ratio, an electron temperature of 22,400 K and an electron density of log n(e) = 4.62 are obtained for the inner He+2 region of NGC 7027. The Ar V 13.09-mu-m/7008 angstrom line ratio in conjunction with the O IV 25.87-mu-m/1402 A line ratio gives an electron temperature of 15,400 K and an electron density of log n(e) = 5.25 in the outer He+2 region of NGC 7027.