We study the H-2 cooling emission of forming galaxies and discuss their observability using the future infrared facility Single Aperture Far-Infrared Observatory (SAFIR). Forming galaxies with mass less than or similar to10(11) M-circle dot emit most of their gravitational energy liberated by contraction in molecular hydrogen line radiation, although a large part of thermal energy at virialization is radiated away by the hydrogen Lyalpha emission. For more massive objects, the degree of heating due to dissipation of kinetic energy is so great that the temperature does not drop below 104 K, and the gravitational energy is emitted mainly by the Lyalpha emission. Therefore, the total H-2 luminosity attains the peak value of L-H2 similar to 10(42) ergs s(-1) for forming galaxies whose total mass M-tot similar to 10(11) M-circle dot. If these sources are situated at redshift z similar to 8, they can be detected by rotational lines of 0-0 S(3) at 9.7 mum and 0-0 S(1) at 17 mum by SAFIR. An efficient way to find such H-2 emitters is to look at the Lyalpha emitters, since the brightest H-2 emitters are also luminous in Lyalpha emission.