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 H _ { 2 } 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 H _ { 2 } .
We simulate a 1D plane-parallel atmosphere to estimate fluxes for the 140 observed H _ { 2 } emission lines and to reconstruct the Ly \alpha emission profile incident upon the warm H _ { 2 } .
The excitation of H _ { 2 } 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 H _ { 2 } 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 ( H _ { 2 } ) = 18.5 ^ { +1.2 } _ { -0.8 } , a temperature T = 2500 ^ { +700 } _ { -500 } 
K , and a filling factor of H _ { 2 } , as seen by the source of Ly \alpha emission , of 0.25 \pm 0.08 ( 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 .