We present X-ray bolometric correction factors, $kappa_{Bol}$ ($equiv L_{Bol}/L_X$), for Compton-thick (CT) active galactic nuclei (AGN) with the aim of testing AGN torus models, probing orientation effects, and estimating the bolometric output of the most obscured AGN. We adopt bolometric luminosities, $L_{Bol}$, from literature infrared (IR) torus modeling and compile published intrinsic 2--10 keV X-ray luminosities, $L_{X}$, from X-ray torus modeling of NuSTAR data. Our sample consists of 10 local CT AGN where both of these estimates are available. We test for systematic differences in $kappa_{Bol}$ values produced when using two widely used IR torus models and two widely used X-ray torus models, finding consistency within the uncertainties. We find that the mean $kappa_{Bol}$ of our sample in the range $L_{Bol}approx10^{42}-10^{45}$ erg/s is log$_{10}kappa_{Bol}=1.44pm0.12$ with an intrinsic scatter of $sim0.2$ dex, and that our derived $kappa_{Bol}$ values are consistent with previously established relationships between $kappa_{Bol}$ and $L_{Bol}$ and $kappa_{Bol}$ and Eddington ratio. We investigate if $kappa_{Bol}$ is dependent on $N_H$ by comparing our results on CT AGN to published results on less-obscured AGN, finding no significant dependence. Since many of our sample are megamaser AGN, known to be viewed edge-on, and furthermore under the assumptions of AGN unification whereby unobscured AGN are viewed face-on, our result implies that the X-ray emitting corona is not strongly anisotropic. Finally, we present $kappa_{Bol}$ values for CT AGN identified in X-ray surveys as a function of their observed $L_X$, where an estimate of their intrinsic $L_{X}$ is not available, and redshift, useful for estimating the bolometric output of the most obscured AGN across cosmic time.
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