We report 1981–1984 thermal infrared observations of 10 Io eclipse reappearances and three eclipse disappearances. Absolute calibration errors were estimated from measurements of Callisto during nine of the eclipses with the following values: 5% at 8.7, 10.2, 12.5, and 20 μm; and 15% at 30 μm. The longer wavelength (8.7, 10.2, 12.5, 20, and 30 μm) eclipse data were used to determine not only the thermal radiation from the volcanoes, but also to find the best thermophysical parameters by a least-squares fitting procedure. No simple thermophysical model capable of fitting all wavelengths simultaneously was found. We found that adequate fitting of the eclipse cooling and heating curves requires not only vertically inhomogeneous models, but also models that are horizontally inhomogeneous at least in the sense of requiring two different albedo regimes. The best model required a variation of the thermophysical parameters between the light and dark albedo components. The thermal inertia of the bright component was nearly 10 times that of the dark component and required a vertically inhomogeneous surface. The dark component's surface was, however, homogeneous. It is shown from the improvement in the sum of the squares of the residuals that the differences of parameters between light and dark regions are significant at the 99.9% level. A major result of this paper is the accurate determination of the volcanic heat radiation for the sub-Jupiter hemisphere. We were able to find solutions for the temperature, effective radiating area, and longitude separately for a high-temperature and a low-temperature volcanic source. The longitudes of either of these sources, when the data were sufficient to make significant determinations, lie within a few degrees of the Loki volcano. The area of the low-temperature source is approximately that of the lava lake seen in Voyager photographs. We believe that Loki is the primary source of excess thermal radiation seen in eclipses of Io, but based on Voyager results it, most likely, is not the only source contributing to the eclipse flux. We have performed a careful evaluation of errors and find that the statistical uncertainty of the total volcanic flux from the Loki region can be as low as 3 to 9% when multiple eclipses, including both disappearances and reappearances, are observed. When comparing one year's data with another, the uncertainty associated with the flux calibration is not involved and only the statistical uncertainty is applicable to the comparison. We have studied the variability of the thermal emission of the volcanoes seen on the sub-Jupiter hemisphere and find that a solution based on the data of W. Sinton, A. Tokunaga, E. Becklin, I. Gatley, T. Lee, and C. Lonsdale (1980, Science 210, 1015–1017) and on the data of D. Morrison and C. Telesco (1980, Icarus 44, 226–233) gives a total flux that is considerably more than that which we find for 1981, 1982, 1983, and 1984 or the Voyager results. Our data for the last four enumerated years give little evidence, by themselves, for variability of the total volcanic flux from the sib-Jupiter hemisphere.