We present an analysis of thermal emission from comet 162P/Siding Spring (P/2004 TU12) measured during its discovery apparition in 2004 December. The comet showed no dust coma at this time, so we have sampled emission from the comet's nucleus. Observations using the Mid-Infrared Spectrometer and Imager (MIRSI) were performed at NASA's Infrared Telescope Facility, where the peak of the comet's spectral energy distribution was observed between 8 and 25 μm. In combination with the three near-IR spectra presented by Campins and coworkers (in the companion to this paper) that show the Wien-law tail of the thermal emission, the data provide powerful constraints on surface properties of the nucleus. We find that the nucleus's effective radius is 6.0+/-0.8 km. This is one of the largest radii known among Jupiter-family comets, which is unusual considering that the comet was discovered only recently. Its geometric albedo is 0.059+/-0.023 in the H band, 0.037+/-0.014 in the R band, and 0.034+/-0.013 in the V band. We also find that the nucleus of 162P has little IR beaming, and this implies that the nucleus has low thermal inertia. Including all near-IR spectra yields a beaming parameter η of 1.01+/-0.20. This result is in agreement with others showing that cometary nuclei have low thermal inertia and little IR beaming. If confirmed for many nuclei, the interpretation of radiometry may not be as problematic as feared.