We measure the temperature of warm gas at planet-forming radii in the disk around the classical T Tauri star (CTTS) TW Hya by modeling the H2 fluorescence observed in Hubble Space Telescope Space Telescope Imaging Spectrograph and Far Ultraviolet Spectroscopic Explorer spectra. Strong Lyα emission irradiates a warm disk surface within 2 AU of the central star and pumps certain excited levels of H2. We simulate a one-dimensional plane-parallel atmosphere to estimate fluxes for the 140 observed H2 emission lines and to reconstruct the Lyα emission profile incident upon the warm H2. The excitation of H2 can be determined from relative line strengths by measuring self-absorption in lines with low-energy lower levels, or by reconstructing the Lyα profile incident upon the warm H2 using the total flux from a single upper level and the opacity in the pumping transition. Based on those diagnostics, we estimate that the warm disk surface has a column density of log N(H2) = 18.5, a temperature T = 2500 K, and a filling factor of H2, as seen by the source of Lyα emission, of 0.25 ± 0.08 (all 2 σ error bars). TW Hya produces approximately 10-3 L☉ in the FUV, about 85% of which is in the Lyα emission line. From the H I absorption observed in the Lyα emission, we infer that dust extinction in our line of sight to TW Hya is negligible.