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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 bystrong detections of the [OIII]$\lambda$4363 auroral emission line across alarge spatial extent of Mrk 1486, reveal a clear negative minor axis $T_e$gradient in which temperature decreases with increasing distance from the diskplane. We find that the lowest metallicity spaxels lie near the extremes of themajor axis, while the highest metallicity spaxels lie at large spatial offsetsalong the minor axis. This is consistent with a picture in which lowmetallicity inflows dilute the metallicity at the edges of the major axis ofthe disk, while star formation drives metal-enriched outflows along the minoraxis. 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 madesimultaneously for inflowing, outflowing, and inner disk ISM gas usingconsistent $T_e$-based methodology. These measurements provide unique insightinto how baryon cycle processes contribute to the assembly of a galaxy like Mrk1486.

The DUVET Survey: Direct $T_e$-based metallicity mapping of metal-enriched outflows and metal-poor inflows in Mrk 1486