  We measure the temperature of warm gas at planet-forming radii in the disk
around the classical T Tauri star (CTTS) TW Hya by modelling the H2
fluorescence observed in HST/STIS and FUSE spectra. Strong Ly-alpha emission
irradiates a warm disk surface within 2 AU of the central star and pumps
certain excited levels of H2. We simulate a 1D plane-parallel atmosphere to
estimate fluxes for the 140 observed H2 emission lines and to reconstruct the
Ly-alpha 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 Ly-alpha 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^{+1.2}_{-0.8}, a temperature T=2500^{+700}_{-500} K, and a filling
factor of H2, as seen by the source of Ly-alpha emission, of 0.25\pm0.08 (all
2-sigma error bars). TW Hya produces approximately 10^{-3} L_\odot in the FUV,
about 85% of which is in the Ly-alpha emission line. From the H I absorption
observed in the Ly-alpha emission, we infer that dust extinction in our line of
sight to TW Hya is negligible.
