Phase curve measurements provide a global view of the composition, thermal structure, and dynamics of exoplanet atmospheres. Although most of the dozens of phase curve measurements made to date are of large, massive hot Jupiters, there is considerable interest in probing the atmospheres of the smaller planets that are the more typical end product of planet formation. One such planet is the ultra-hot Neptune LTT 9779b, a rare denizen of the Neptune desert. A companion paper presents the planets secondary eclipses and day-side thermal emission spectrum; in this work we describe the planets optical and infrared phase curves, characterized using Spitzer and TESS photometry. We detect LTT 9779bs thermal phase variations at 4.5um, finding a phase amplitude of 358+/-106 ppm and a longitude of peak emission -10 deg +/- 21 deg east of the substellar point. Combined with our secondary eclipse observations, these phase curve measurements imply a 4.5um day-side brightness temperature of 1800+/-120 K, a night-side brightness temperature of 700+/-430 K (<1350 K at 2 sigma confidence), and a day-night brightness temperature contrast of 1110+/-460 K. We compare our data to the predictions of 3D GCMs and to similar observations of hot Jupiters experiencing similar levels of stellar irradiation. Though not conclusive, our measurement of its small 4.5um phase offset, the relatively large amplitude of the phase variation, and the qualitative differences between our targets day-side emission spectrum and those of hot Jupiters of similar temperatures all suggest a super-Solar atmospheric metallicity for LTT 9779b, as might be expected given its size and mass. Finally, we provide a refined ephemeris (P=0.79207022+/-0.00000069 d, T0=2458783.51636+/-0.00027, BJD_TDB) to enable efficient scheduling of future observations to further characterize the atmosphere of this intriguing planet. (abstract abridged)
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