We report one of the first extragalactic observations of electron temperature variations across a spiral arm. Using Multi Unit Spectroscopic Explorer mosaic observations of the nearby galaxy NGC 1672, we measure the [N II]λ5755 auroral line in a sample of 80 H II regions in the eastern spiral arm of NGC 1672. We discover systematic temperature variations as a function of distance perpendicular to the spiral arm. The electron temperature is lowest on the spiral arm itself and highest on the downstream side. Photoionization models of different metallicity, pressure, and age of the ionizing source are explored to understand what properties of the interstellar medium drive the observed temperature variations. An azimuthally varying metallicity appears to be the most likely cause of the temperature variations. The electron temperature measurements solidify recent discoveries of azimuthal variations of oxygen abundance based on strong lines, and rule out the possibility that the abundance variations are artifacts of the strong-line calibrations.