  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$_{10}\kappa_{Bol}=1.44\pm0.12$
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.
