Faint X-ray emission from hot plasma ( T _ { x } > 10 ^ { 6 } K ) has been detected extending outward a few arcseconds along the optically-delineated jets of some classical T Tauri stars including RY Tau . The mechanism and location where the jet is heated to X-ray temperatures is unknown . We present high spatial resolution Hubble Space Telescope ( HST ) far-ultraviolet long-slit observations of RY Tau with the slit aligned along the jet . The primary objective was to search for C IV emission from warm plasma at T _ { CIV } \sim 10 ^ { 5 } K within the inner jet ( < 1 ^ { \prime \prime } ) that can not be fully-resolved by X-ray telescopes . Spatially-resolved C IV emission is detected in the blueshifted jet extending outward from the star to 1 ^ { \prime \prime } and in the redshifted jet out to 0 ^ { \prime \prime } .5 . C IV line centroid shifts give a radial velocity in the blueshifted jet of - 136 \pm 10 km s ^ { -1 } at an offset of 0 ^ { \prime \prime } .29 ( 39 au ) and deceleration outward is detected . The deprojected jet speed is subject to uncertainties in the jet inclination but values \stackrel { \raisebox { -0.86 pt } { $ \textstyle > $ } } { \sim } 200 km s ^ { -1 } are likely . The mass-loss rate in the blueshifted jet is at least \dot { M } _ { jet,blue } = 2.3 \times 10 ^ { -9 } M _ { \odot } yr ^ { -1 } , consistent with optical determinations . We use the HST data along with optically-determined jet morphology to place meaningful constraints on candidate jet-heating models including a hot-launch model in which the jet is heated near the base to X-ray temperatures by an unspecified ( but probably magnetic ) process , and downstream heating from shocks or a putative jet magnetic field .