  We report the results of a search for pure rotational molecular hydrogen
emission from the circumstellar environments of young stellar objects with
disks using the Texas Echelon Cross Echelle Spectrograph (TEXES) on the NASA
Infrared Telescope Facility and the Gemini North Observatory. We searched for
mid-infrared H2 emission in the S(1), S(2), and S(4) transitions. Keck/NIRSPEC
observations of the H2 S(9) transition were included for some sources as an
additional constraint on the gas temperature. We detected H2 emission from 6 of
29 sources observed: AB Aur, DoAr 21, Elias 29, GSS 30 IRS 1, GV Tau N, and HL
Tau. Four of the six targets with detected emission are class I sources that
show evidence for surrounding material in an envelope in addition to a
circumstellar disk. In these cases, we show that accretion shock heating is a
plausible excitation mechanism. The detected emission lines are narrow (~10
km/s), centered at the stellar velocity, and spatially unresolved at scales of
0.4 arcsec, which is consistent with origin from a disk at radii 10-50 AU from
the star. In cases where we detect multiple emission lines, we derive
temperatures > 500 K from ~1 M_earth of gas. Our upper limits for the
non-detections place upper limits on the amount of H2 gas with T > 500 K of
less than a few Earth masses. Such warm gas temperatures are significantly
higher than the equilibrium dust temperatures at these radii, suggesting that
the gas is decoupled from the dust in the regions we are studying and that
processes such as UV, X-ray, and accretion heating may be important.
