  We present electron temperature ($T_e$) maps for the edge-on system Mrk 1486,
affording "direct-method" gas-phase metallicity measurements across
$5.\!\!^{\prime\prime}8$ (4.1 kpc) along the minor axis and
$9.\!\!^{\prime\prime}9$ (6.9 kpc) along the major axis. These maps, enabled by
strong detections of the [OIII]$\lambda$4363 auroral emission line across a
large spatial extent of Mrk 1486, reveal a clear negative minor axis $T_e$
gradient in which temperature decreases with increasing distance from the disk
plane. We find that the lowest metallicity spaxels lie near the extremes of the
major axis, while the highest metallicity spaxels lie at large spatial offsets
along the minor axis. This is consistent with a picture in which low
metallicity inflows dilute the metallicity at the edges of the major axis of
the disk, while star formation drives metal-enriched outflows along the minor
axis. We find that the outflow metallicity in Mrk 1486 is 0.20 dex (1.6 times)
higher than the average ISM metallicity, and more than 0.80 dex (6.3 times)
higher than metal-poor inflowing gas, which we observe to be below 5 %
$Z_\odot$. This is the first example of metallicity measurements made
simultaneously for inflowing, outflowing, and inner disk ISM gas using
consistent $T_e$-based methodology. These measurements provide unique insight
into how baryon cycle processes contribute to the assembly of a galaxy like Mrk
1486.
