Faint X-ray emission from hot plasma (T_x > 10⁶K) 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 jets are heated to X-ray temperatures are 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 _{C iv} ∼ 10⁵ K within the inner jet (<1″) that cannot 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″ and in the redshifted jet out to 0.″5. C iv line centroid shifts give a radial velocity in the blueshifted jet of −136 ± 10 km s⁻¹ at an offset of 0.″29 (39 au) and deceleration outward is detected. The deprojected jet speed is subject to uncertainties in the jet inclination, but values ≳200 km s⁻¹ are likely. The mass-loss rate in the blueshifted jet is at least M˙_jet,blue = 2.3 × 10^{− 9} M_⊙ 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.