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We have made 20.0 $\mu$m imaging array observations of the core of the Sgr A West complex with the 58 $\times$ 62 pixel array camera system developed at NASA/Goddard. The image was analyzed using four methods: 1) adding and subtracting a set of synthetic point sources of decreasing brightness at the position of Sgr A* to determine a threshold of detection, 2) subtracting a smoothed version of the same image to remove the extended source component, 3) subtracting a version of the same image with the position of Sgr A* patched over by two-dimensional interpolation, and 4) deconvolution of the image using the Richardson-Lucy algorithm. As a result of this analysis, we conclude that no contribution can be attributed to Sgr A* at 20 $\mu$m above an observed brightness upper limit of 0.3 Jy arcsec$^{-2}$, or a total observed point source flux density upper limit of 1.0 Jy, with an uncertainty estimated at about $\pm$0.5 Jy. Among possible implications of the present observations, our result clearly constrains models for either thermal dust emission or self-absorbed synchrotron emission. Our upper limit of $\sim1$ Jy could eliminate temperatures $ T > 2 \times 10^4$ K in accretion disk models of Sgr A*.
