Multi-temperature thermal plasmas have often to be considered to account for the nonequilibrium effects. Recently Andre et al. have developed the calculation of concentrations in a multi-temperature plasma by artificially separating the partition functions into a product by assuming that the excitation energies are those of the lower levels (electronic, vibration, and rotation). However, at equilibrium, differences, increasing with temperature, can be observed between partition functions calculated rigorously and with their method. This paper presents a modified method where it has been assumed that the preponderant rotational energy is that of the vibrational level v = 0 of the ground electronic state and the preponderant vibrational energy is that of the ground electronic state. The internal partition function can then be expressed as a product of series expressions. At equilibrium for N-2 and N-2(+) partition functions the values calculated with our method differ by less than 0.1% from those calculated rigorously. The calculation has been limited to three temperatures : heavy species T-h, electrons T-e, and vibrational T-v temperatures. The plasma composition has been calculated by minimizing the Gibbs free enthalpy with the steepest descent numerical technique. The nonequilibrium properties have been calculated using the method of Devote, modified by Bonnefoi and Aubreton. The ratio theta = T-e/T-h was varied between 1 and 2 as well as the ratio theta(upsilon) = T-upsilon/T-h for a nitrogen plasma. At equilibrium the corresponding equilibrium transport properties of Ar and N-2 are in good agreement with those of Devote and Murphy except for T > 10,000 K where we used a different interaction potential for N-N+. The effects of theta(v) and theta(e) on thermodynamic and transport properties of N-2 are then discussed.