We report high spectral resolution Australia Telescope Compact Array HI 21 cm observations resulting in the detection of the warm neutral medium ( WNM ) of the Galaxy in absorption against two extragalactic radio sources , PKS 1814 - 637 and PKS 0407 - 658 . The two lines of sight were selected on the basis of the simplicity of their absorption profiles and the strength of the background sources ; the high velocity resolution of the spectra then enabled us to estimate the kinetic temperatures of the absorbing gas by fitting multiple Gaussians to the absorption profiles . Four separate WNM components were detected toward the two sources , with peak optical depths \tau _ { max } = ( 1.0 \pm 0.08 ) \times 10 ^ { -2 } , ( 1.4 \pm 0.2 ) \times 10 ^ { -3 } , ( 2.2 \pm 0.5 ) \times 10 ^ { -3 } and ( 3.4 \pm 0.5 ) \times 10 ^ { -3 } and kinetic temperatures T _ { k } = 3127 \pm 300 K , 3694 \pm 1595 K , 3500 \pm 1354 K and 2165 \pm 608 K respectively . All four components were thus found to have temperatures in the thermally unstable range 500 < T _ { k } < 5000 K ; this suggests that thermal equilibrium has not been reached throughout the WNM .