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We present new thermophysical model (TPM) fits of 1,847 asteroids, deriving thermal inertia, diameter, and Bond and visible geometric albedo. We use thermal flux measurements obtained by the Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010; Mainzer et al. 2011) during its fully cryogenic phase, when both the 12$μ$m (W3) and 22$μ$m (W4) bands were available. We take shape models and spin information from the Database of Asteroid Models from Inversion Techniques (DAMIT; Ďurech et al. 2010) and derive new shape models through lightcurve inversion and combining WISE photometry with existing DAMIT lightcurves. When we limit our sample to the asteroids with the most reliable shape models and thermal flux measurements, we find broadly consistent thermal inertia relations with recent studies. We apply fits to the diameters $D$ (km) and thermal inertia $Γ$ (J m$^{-2}$ s$^{-0.5}$ K$^{-1}$) normalized to 1 au with a linear relation of the form $\log[Γ]=α+β\log[D]$, where we find $α= 2.667 \pm 0.059$ and $β= -0.467 \pm 0.044$ for our sample alone and $α= 2.509 \pm 0.017$ and $β= -0.352 \pm 0.012$ when combined with other literature estimates. We find little evidence of any correlation between rotation period and thermal inertia, owing to the small number of slow rotators to consider in our sample. While the large uncertainties on the majority of our derived thermal inertia only allow us to identify broad trends between thermal inertia and other physical parameters, we can expect a significant increase in high-quality thermal flux measurements and asteroid shape models with upcoming infrared and wide-field surveys, enabling even more thermophysical modeling of higher precision in the future.