Infrared spectrum of the v(2) fundamental band of H-3(+) in high rotational levels has been studied. Three motives for this study were (i) to provide laboratory data for the observation of astronomical objects in which a large abundance of H-3(+) exists at high temperature, (ii) to study kinetic energy distribution of H-3(+) in plasmas and to determine its rotational and translational temperatures, and (iii) to provide information on high rovibrational states for the variational calculations on the intramolecular dynamic of H-3(+). In order to increase the kinetic temperature, water-cooled plasmas with helium dominated gas mixtures with He/H-2 similar to 5/0.6 torr were used. The observed rotational level in the ground state with the highest rotational quantum numbers was J = K = 15 which has the rotational energy of 5091.6 cm(-1). It was found from the observed relative intensities of the rovibrational transitions and linewidths that H-3(+) in the plasmas were in approximate thermal equilibrium with both rotational and translational temperature of similar to 1000 K. On the contrary, an analysis of the relative intensities of the H-3(+) spectral lines observed in our previous study of carbocation spectroscopy showed nonthermal rotational distribution. A semiquantitative discussion is given on the observed results.