It is proposed that the rotational and vibrational temperatures of H 2 can be derived from the fitting to the H2 Fulcher band (d3Πu - - a3 Σg) line emissions. However, the fitting relies on the employed spontaneous radiative transition probabilities and the excitation rate coefficients, which are dependent on the vibrational and rotational quanta in each electronic state. From our study, it is found that, in low temperature plasmas both the Fulcher-α radiative transition and the electron impact excitation to the d 3Πu state from the ground electronic state deviate significantly from the Franck-Condon approximation. The vibrationally resolved complete sets of the cross sections are calculated based on the semi-classical Gryzinski theory, and the Fulcher band transition probabilities are obtained based on the newest published data on the electronic transition moment and the solution to the radial Schrödinger equation. The fitting to experimental line emissions shows that Boltzmann's Law can be employed for the distribution of vibrational (in lower level), and particularly for the rotational, populations in the ground electronic state of H2 in low temperature plasmas.