  Brightest Cluster Galaxies (BCGs) are believed to have assembled most of
their stars early in time and, therefore, should be passively evolving at low
redshifts and appear "red-and-dead." However, there have been reports that a
minority of low-redshift BCGs still have ongoing star formation rates (SFR) of
a few to even $\sim$100 $M_\odot/yr$. Such BCGs are found in "cool-core" ("CC")
clusters, and their star formation is thought to be fueled by "cooling flow."
To further investigate the implications of low-redshift, star-forming BCGs, we
perform a systematic search using the 22$\mu$m data ("W4" band) from the
Wide-field Infrared Survey Explorer (WISE) on the GMBCG catalog, which contains
55,424 BCGs at $0.1\lesssim z\lesssim 0.55$ identified in the Sloan Digital Sky
Survey (SDSS). Our sample consists of 389 BCGs that are bright in W4
("W4BCGs"), most being brighter than 5 mJy. While some ($\lesssim 20\%$) might
host AGN, most W4BCGs should owe their strong mid-IR emissions to
dust-enshrouded star formation. Their median total IR luminosity ($L_{IR}$) is
$5\times10^{11} L_{\odot}$ (SFR $\sim$50 $M_{\odot}/yr)$, and 27\% of the whole
sample has $L_{IR}>10^{12} L_{\odot}$ (SFR $>$100 $M_{\odot}/yr$). Using ten
W4BCGs that have Chandra X-ray data, we show that seven of them are possibly in
CC clusters. However, in most cases (five out of seven) the mass deposition
rate cannot account for the observed SFR. This casts doubt to the idea that
cooling flows are the cause of the star formation in non-quiescent BCGs.
