  More than a thousand warm debris disks have been detected as infrared excess
at mid-infrared wavelengths, and their frequencies have been obtained for
various spectral types of stars. However, the dependence of the frequencies on
spectral type is still debated because the number of stars with significant and
detectable infrared excess is limited. Herein, we present the largest
systematic search for infrared excess using data from Gaia, WISE, and Spitzer.
We identified 373, 485, and 255-reliable infrared excesses in the mid-infrared
archival data at wavelengths of 12, 22, and 24 $\mu$m for WISE/$W3$, $W4$, and
Spitzer/MIPS ch1, respectively. Although we confirmed that more massive stars
tend to show higher frequencies of debris disks, these disk frequencies are
relatively flat for both low- and intermediate-mass stars, with a jump at 7000
K for all three wavelengths. Assuming that bright, warm debris disks have
lifetimes of a few to several hundred million years, the disk frequency can be
understood as the ratio between the timescale and the upper limits of the
sample ages. We also found that intermediate-mass stars with infrared excess
tend to be bluer and fainter along the evolutionary track than those without,
implying that massive stars hosting debris disks are relatively young, with an
isochronal age of approximately 500 Myr. These tendencies are reasonably
explained by a standard scenario in which debris disks are likely to be
produced by collisions of planetesimals in early stages of stellar evolution,
such as the Late Heavy Bombardment.
