  A near surface thermal model for Arrokoth is developed based on the recently
released $10^5$ facet model of the body. This thermal solution takes into
account Arrokoth's surface re-radiation back onto itself. The solution method
exploits Arrokoth's periodic orbital character to develop a thermal response
using a time-asymptotic solution method, which involves a Fourier transform
solution of the heat equation, an approach recently used by others. We display
detailed thermal solutions assuming that Arrokoth's near surface material's
thermal inertia ${\cal I} = $ 2.5 W/m$^{-2}$K$^{-1}$s$^{1/2}$. We predict that
at New Horizons' encounter with Arrokoth its encounter hemisphere surface
temperatures were $\sim$ 57-59 K in its polar regions, 30-40 K on its
equatorial zones, and 11-13 K for its winter hemisphere. Arrokoth's orbitally
averaged temperatures are around 30-35 K in its polar regions, and closer to 40
K near its equatorial zones. Thermal reradiation from the surrounding surface
amounts to less than 5\% of the total energy budget, while the total energy
ensconced into and exhumed out Arrokoth's interior via thermal conduction over
one orbit is about 0.5\% of the total energy budget. As a generalized
application of this thermal modeling together with other KBO origins
considerations, we favor the interpretation that New Horizons' REX instrument's
$29 \pm 5$K brightness temperature measurement is consistent with Arrokoth's
near surface material's being made of sub-to-few mm sized tholin-coated
amorphous \water ice grains with 1 W/m$^{-2}$K$^{-1}$s$^{1/2}$ $< {\cal I} <
$10-20 W/m$^{-2}$K$^{-1}$s$^{1/2}$, and which are characterized by an X-band
emissivity in the range 0.9 and 1.
