Observations of the nucleus of 67P/Churyumov-Gerasimenko in the millimeter-wave continuum have been obtained by the Microwave Instrument for the Rosetta Orbiter (MIRO). We present data obtained at wavelengths of 0.5 mm and 1.6 mm during September 2014 when the nucleus was at heliocentric distances between 3.45 and 3.27 AU. The data are fit to simple models of the nucleus thermal emission in order to characterize the observed behavior and make quantitative estimates of important physical parameters, including thermal inertia and absorption properties at the MIRO wavelengths. MIRO brightness temperatures on the irregular surface of 67P are strongly affected by the local solar illumination conditions, and there is a strong latitudinal dependence of the mean brightness temperature as a result of the seasonal orientation of the comet's rotation axis with respect to the Sun. The MIRO emission exhibits strong diurnal variations, which indicate that it arises from within the thermally varying layer in the upper centimeters of the surface. The data are quantitatively consistent with very low thermal inertia values, between 10-30 J K-1 m-2 s-1/2, with the 0.5 mm emission arising from 1 cm beneath the surface and the 1.6 mm emission from a depth of 4 cm. Although the data are generally consistent with simple, homogeneous models, it is difficult to match all of its features, suggesting that there may be some vertical structure within the upper few centimeters of the surface. The MIRO brightness temperatures at high northern latitudes are consistent with sublimation of ice playing an important role in setting the temperatures of these regions where, based on observations of gas and dust production, ice is known to be sublimating.