With the Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010), we have observed over 157,000 minor planets (Mainzer et al. 2011). Included in these are a number of near-Earth objects, Main Belt Asteroids, and irregular satellites which have well-measured physical properties via radar, occultation and in situ imaging. We have used these objects to validate models of thermal models using the WISE measurements, as well as the color corrections derived in Wright et al. (2010) for the four WISE bandpasses as a function of effective temperature. We have used 50 objects with diameters measured by radar, occultation or in situ imaging to characterize the systematic errors implicit in using the WISE data with a faceted spherical NEATM model to compute diameters and albedos. By using the previously measured diameters and H magnitudes with a spherical NEATM model, we compute the predicted fluxes after applying the color corrections given in Wright et al. (2010) in the WISE bands and compare them to the measured magnitudes. We find minimum systematic flux errors of 5-10%, yielding minimum relative diameter and albedo errors of ~10% and ~20%, respectively. Visible albedos for the objects are computed and compared to the albedos at 3.4 and 4.6 microns, which contain a mix of reflected sunlight and thermal emission for most asteroids. We derive a linear relationship between subsolar temperature and effective temperature, which allows the color corrections given in Wright et al. (2010) to be used for asteroids by computing only subsolar temperature instead of a faceted thermal model. The thermal models derived in this paper are not intended to supplant previous measurements made using radar or spacecraft imaging; rather, we have used them to characterize the errors that should be expected when computing diameters and albedos of WISE asteroids using a spherical NEATM model.