We use high-resolution UV spectra taken by the Space Telescope Imaging Spectrograph instrument on board the Hubble Space Telescope to study the 5.5 pc line of sight to the K0 V star 36 Oph A . The one interstellar component detected for this line of sight has a velocity inconsistent with the local interstellar cloud ( LIC ) flow vector , but consistent with the flow vector of the so-called G cloud , a very nearby warm cloud in the Galactic Center direction . From our data , we measure the following values for the interstellar temperature , nonthermal velocity , H I column density , and D/H value : T = 5900 \pm 500 K , \xi = 2.2 \pm 0.2 km s ^ { -1 } , \log N _ { H } = 17.85 \pm 0.15 , and { D / H } = ( 1.5 \pm 0.5 ) \times 10 ^ { -5 } . The temperature of the G cloud is somewhat lower than that of the LIC , and Mg and Fe depletions are also lower , but the D/H value appears to be the same . Based on upper limits for the LIC absorption , we estimate the distance to the edge of the LIC to be d _ { edge } < 0.19 pc , which the Sun will reach in t _ { edge } < 7400 yrs . The H I Lyman- \alpha absorption line has properties inconsistent with those of the other absorption lines , indicating the presence of one or more absorption components not seen in the other lines . We present evidence that hot neutral hydrogen local to both the Sun and the star is responsible for the excess Lyman- \alpha absorption . This hot H I is created by the interaction between the ISM and the winds of the Sun and 36 Oph A . The observed line of sight lies only 12 ^ { \circ } from the upwind direction of the LIC flow vector , where hydrodynamic models of the heliosphere suggest that heliospheric H I absorption should be particularly prominent . The properties of the heliospheric absorption ( T = 38 , 000 \pm 8000 K and \log N _ { H } = 14.6 \pm 0.3 ) are consistent with previous measurements of this absorption for the \alpha Cen line of sight 52 ^ { \circ } from the upwind direction .