  The infrared Mg I lines near 12 microns are a pair of emission lines which
are magnetically sensitive and have been used to measure solar magnetic fields.
Here we calculate the response of the Mg I 12.32 $\mu$m line during a flare and
find that in our modeling this line has a complicated behavior. At the
beginning of the flare heating, this line shows an intensity dimming at the
line center. The intensity then increases when heating continues, with
increasing contributions from the heated layers in the chromosphere. The line
formation height and the line width also increase as a result. As for the
polarized line profiles, we find that flare heating tends to decrease the
Zeeman splitting width and attenuates the Stokes $V$ lobe intensity. The wider
features in the Stokes $V$ profiles are more pronounced during flare heating,
which should be considered when performing magnetic field inversions.
