  We present theoretical calculations of the thermal conductivity for the
accidental degeneracy and enlarged symmetry group models that have been
proposed to explain the phase diagram of UPt3. The order parameters for these
models possess point nodes or cross nodes, reflecting the broken symmetries of
the ground state. These broken symmetries lead to robust predictions for the
ratio of the low-temperature thermal conductivity for heat flow along the c
axis and in the basal plane. The anisotropy of the heat current response at low
temperatures is determined by the phase space for scattering by impurities. The
measured anisotropy ratio, $\kappa_c/\kappa_b$, provides a strong constraint of
theoretical models for the ground state order parameter. The accidental
degeneracy and enlarged symmetry group models based on no spin-orbit coupling
do not account for the thermal conductivity of UPt3. The models for the order
parameter that fit the experimental data for the c and b directions of the heat
current are the 2D E1g and E2u models, for which the order parameters possess
line nodes in the ab-plane and point nodes along the c axis, and the A1g+E1g
model of Zhitomirsky and Ueda. This model spontaneously breaks rotational
symmetry in theab-plane below Tc2 and predicts a large anisotropy for the
$ab$-plane heat current.
