Using the Infrared Spectrograph on board the Spitzer Space Telescope, we have detected emission in the S(0), S(1), and S(2) pure-rotational (v = 0-0) transitions of molecular hydrogen (H₂) toward six positions in two translucent high Galactic latitude clouds, DCld 300.2-16.9 and LDN 1780. The detection of these lines raises important questions regarding the physical conditions inside low-extinction clouds that are far from ultraviolet radiation sources. The ratio between the S(2) flux and the flux from polycyclic aromatic hydrocarbons (PAHs) at 7.9 mum averages 0.007 for these six positions. This is a factor of about four higher than the same ratio measured toward the central regions of non-active Galaxies in the Spitzer Infrared Nearby Galaxies Survey. Thus, the environment of these translucent clouds is more efficient at producing rotationally excited H₂ per PAH-exciting photon than the disks of entire galaxies. Excitation analysis finds that the S(1) and S(2) emitting regions are warm (T >~ 300 K), but comprise no more than 2% of the gas mass. We find that UV photons cannot be the sole source of excitation in these regions and suggest mechanical heating via shocks or turbulent dissipation as the dominant cause of the emission. The clouds are located on the outskirts of the Scorpius-Centaurus OB association and may be dissipating recent bursts of mechanical energy input from supernova explosions. We suggest that pockets of warm gas in diffuse or translucent clouds, integrated over the disks of galaxies, may represent a major source of all non-active galaxy H₂ emission.