The Goddard Infrared Array Camera was used to obtain a high resolution image of the nucleus of NGC 1068 at 12.4 microns. In addition, the peak emission at 12.4 microns relative to the peak of the optical continuum was determined. The distribution of the 12.4 micron emission relates to both the forbidden O III 5007A 'ionization cone' and the optical continuum emission imaged by HST. This distribution is also found to have an alignment perpendicular to the plane of a putative molecular torus. It is suggested that the extended mid-infrared emission is thermal radiation from dust in circumnuclear clouds heated by the collimated optical/UV AGN source. A portion of the unresolved 12.4 micron emission possibly originates from the torus. The infrared emission peak is found to coincide with the apex of the ionization cone, which is presumed to be the location of the torus.