The energy spectra of electrons released in thermal energy (~ 50 meV) ionizing collisions of He* (2 iS, 23S) with H 2 have been measured with high resolution and low background. Based on a detailed data analysis, we report accurate H~ (v') vibrational populations P(v') for both He*(21S)+Hz (v'=O-lO) and He*(23S)+H2(v'=0-15) and the spectral shape S(e) for the individual vibrational peaks. The vibrational populations P(v') are quite similar to the Franck-Condon factors fv, 0 for unperturbed H 2 (v" = 0) "-~ H + (v') transitions, but, more in detail, the ratios P(v')/f~,o show a characteristically different v'-dependence for He*(23S), He*(21S), and HeI~(58.4 nm) ionization. The vibrational level separations in the He*(21S, 23S) + H 2 spectra agree with those in the HeI photoelectron spectrum to within 1-2 meV. The spectral shapes S(e) are characteristically different for He* (2 tS)+ H 2 and He* (23S) + H2, reflecting the respective differences in the entrance channel potentials, as determined previously in ab initio calculations and from scattering experiments.