One of the torus characteristics of most interest for understanding torus energization is its electron temperature T-e. Yet deriving T-e has always been difficult because the measured quantity (emission brightness) is controlled jointly by T-e and other unknowns, such as ion and electron density. In order to solve this problem, we have used a new technique to estimate T-e from spectral images of the Io plasma torus in the 350 to 700 Angstrom region obtained by the Extreme Ultraviolet Explorer (EUVE), Because of the lack of information available on the collision strengths of important lines between 350 and 600 Angstrom, we have simultaneously attempted to constrain the unknown collision strengths and also to deduce the time-varying torus characteristics by fitting analytic models which exploit the both the commonalities and the variations among the observations. However, because of present limitations of the data set, we can only deduce relative variations in torus T-e, total electron number N-e (a proxy for total torus mass), and ionic composition. In the 1993 - 1995 data set, T-e and N-e were anticorrelated, while total torus luminosity remained steadier than either T-e or N-e. One interpretation of the anticorrelation of N-e and T-e is that torus luminosity may be primarily determined by a relatively constant power-limited energy supply, so that as N-e increases (decreases), T-e sags (surges) in response, This anticorrelation is a constraint on theories of torus energization and transport. There also seems to have been an abrupt 20% decrease in N-e at about the time of the comet Shoemaker-Levy 9 impacts on Jupiter, as though a magnetospheric disturbance had increased the convective loss rate of the torus, but this may well be a coincidence.