H _ { 2 } pure-rotational emission lines are detected from warm ( 100-1500 K ) molecular gas in 17/55 ( 31 % of ) radio galaxies at redshift z < 0.22 observed with the Spitzer IR Spectrograph . The summed H _ { 2 } 0-0 S ( 0 ) -S ( 3 ) line luminosities are L ( \mathrm { H } _ { 2 } ) = 7 \times 10 ^ { 38 } -2 \times 10 ^ { 42 } erg s ^ { -1 } , yielding warm H _ { 2 } masses up to 2 \times 10 ^ { 10 } M _ { \odot } . These radio galaxies , of both FR radio morphological types , help to firmly establish the new class of radio-selected molecular hydrogen emission galaxies ( radio MOHEGs ) . MOHEGs have extremely large H _ { 2 } to 7.7 \mu m PAH emission ratios : L ( H _ { 2 } ) / L ( \mathrm { PAH 7.7 } ) = 0.04 - 4 , up to a factor 300 greater than the median value for normal star-forming galaxies . In spite of large H _ { 2 } masses , MOHEGs appear to be inefficient at forming stars , perhaps because the molecular gas is kinematically unsettled and turbulent . Low-luminosity mid-IR continuum emission together with low-ionization emission line spectra indicate low-luminosity AGNs in all but 3 radio MOHEGs . The AGN X-ray emission measured with Chandra is not luminous enough to power the H _ { 2 } emission from MOHEGs . Nearly all radio MOHEGs belong to clusters or close pairs , including 4 cool core clusters ( Perseus , Hydra , A 2052 , and A 2199 ) . We suggest that the H _ { 2 } in radio MOHEGs is delivered in galaxy collisions or cooling flows , then heated by radio jet feedback in the form of kinetic energy dissipation by shocks or cosmic rays .