We have measured the temperature dependence of the infrared spectra of a hydrogen molecule trapped inside a C(60) cage, H(2)@C(60), in the temperature range from 6 to 300 K and analyzed the excitation spectrum by using a five-dimensional model of a vibrating rotor in a spherical potential. The electric dipole moment is induced by the translational motion of endohedral H(2) and gives rise to an infrared absorption process where one translational quantum is created or annihilated, ΔN = ±1. Some fundamental transitions, ΔN = 0, are observed as well. The rotation of endohedral H(2) is unhindered but coupled to the translational motion. The isotropic and translation-rotation coupling part of the potential are anharmonic and different in the ground and excited vibrational states of H(2). The vibrational frequency and the rotational constant of endohedral H(2) are smaller than those of H(2) in the gas phase. The assignment of lines to ortho- and para-H(2) is confirmed by measuring spectra of a para enriched sample of H(2)@C(60) and is consistent with the earlier interpretation of the low temperature infrared spectra [Mamone et al., J. Chem. Phys. 130, 081103 (2009)].