We report a new study of the nucleus of Comet 2P/Encke, which the CONTOUR spacecraft is scheduled to encounter in November 2003. During the comet's close approach to Earth in July 1997, we measured the mid-infrared thermal and optical scattered continua with data from the TIMMI instrument (imaging) at the ESO 3.6-m telescope (wavelength λ from 8 to 12 µm), the ISOPHOT instrument (photometry) aboard ISO (3.6 µm ≤ λ ≤ 100 µm), and the STIS instrument (imaging) aboard HST (5500 Å ≤ λ ≤ 11000 Å ). The optical images show the nucleus with very little coma contamination, and the ISO photometry allowed us to separate the comatic and nuclear contributions to the ESO images. We used the Standard Thermal Model for slow rotators to calculate an effective nuclear radius of 2.4 km ± 0.3 km. The comet's mid-IR light curve implies a nuclear rotation period of 15.2 h ± 0.3 h, although some subharmonics of this also satisfy the data. If we assume that the nucleus is a triaxial ellipsoid in principal short axis rotation with the axis direction in 1985 as derived by Sekanina (1988, Astron. J. 95, 911), then by combining our data with light curves from the 1980s we find that the nucleus' angular momentum vector migrates, making a would-be circle in less than 81 years, and that one axial ratio is at least 2.6. The nucleus' optical linear phase coefficient is 0.06 mag/degree, making it one of the most phasedarkened objects known. The surface is also rougher than that of