We have conducted an N-band survey of 14 young stars in the \sim 30 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 : ( a ) optically-thick disks with inner hole radii of \lesssim 0.1 AU , ( b ) optically-thin disks with masses of > 10 ^ { -6 } M _ { \oplus } ( in \sim 1-µm-sized grains ) within \lesssim 10 AU of these stars , ( c ) scaled-up analogs of the solar system zodiacal dust cloud with > 4000 \times the emitting area . Our survey was sensitive to dust disks in the terrestrial planet zone with fractional luminosity of log ( L _ { dust } /L _ { * } ) \sim 10 ^ { -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 \sim 20 Myr . We also present N-band photometry for several members of other young associations and a subsample of targets that will be observed with Spitzer Space Telescope by the Formation and Evolution of Planetary Systems ( FEPS ) Legacy Science Program . Lastly , we present an absolute calibration of MIRAC-BLINC for four filters ( L , N , 11.6 , and Q _ { s } ) on the Cohen-Walker-Witteborn system .