We have observed 1H NMR spectra of hydrogen molecules trapped inside modified fullerene cages under cryogenic conditions. Experiments on static samples were performed at sample temperatures down to 4.3 K, while magic-angle-spinning (MAS) experiments were performed at temperatures down to 20 K at spinning frequencies of 15 kHz. Both types of NMR spectra show a large increase in the intramolecular 1H-1H dipolar coupling at temperatures below 50 K, revealing thermal selection of a small number of spatial rotational states. The static and MAS spectra were compared to estimate the degree of sample heating in high-speed cryogenic MAS-NMR experiments. The cryogenic MAS-NMR data show that the site resolution of magic-angle-spinning NMR may be combined with the high signal strength of cryogenic operation and that cryogenic phenomena may be studied with chemical site selectivity.