We have conducted an N-band survey of 14 young stars in the approx30 Myr old Tucana-Horologium association to search for evidence of warm, circumstellar dust disks. Using the MIRAC-BLINC camera on the Magellan I (Baade) 6.5 m telescope, we find that none of the stars have a statistically significant N-band excess compared to the predicted stellar photospheric flux. Using three different sets of assumptions, this null result rules out the existence of the following around these post-T Tauri stars: (1) optically thick disks with inner hole radii of ~0.1 AU, (2) optically thin disks with masses of less than 10 super(-6) M sub(o+) (in approx1 mu m sized grains) within ~10 AU of these stars, and (3) scaled-up analogs of the solar system zodiacal dust cloud with more than 4000 times the emitting area. Our survey was sensitive to dust disks in the terrestrial planet zone with fractional luminosity of log(L sub(dust)/L sub(*)) approx 10 super(-2.9), yet none were found. Combined with results from previous surveys, these data suggest that circumstellar dust disks become so optically thin as to be undetectable at N band before age approx20 Myr. We also present N-band photometry for several members of other young associations and a subsample of targets that will be observed with the Spitzer Space Telescope by the Formation and Evolution of Planetary Systems Legacy Science Program. Finally, we present an absolute calibration of MIRAC-BLINC for four filters (L, N, 11.6, and Q sub(s)) on the Cohen-Walker-Witteborn system.