  Low-temperature electrical and thermal transport, magnetic penetration depth,
and heat capacity measurements were performed on single crystals of the
actinide superconductor UTe2 to determine the structure of the superconducting
energy gap. Heat transport measurements performed with currents directed along
both crystallographic a- and b-axes reveal a vanishingly small residual
fermionic component of the thermal conductivity. The magnetic field dependence
of the residual term follows a rapid, quasi-linear increase consistent with the
presence of nodal quasiparticles, rising toward the a-axis upper critical field
where the Wiedemann-Franz law is recovered. Together with a quadratic
temperature dependence of the magnetic penetration depth up to T/T_c=0.3, these
measurements provide evidence for an unconventional spin-triplet
superconducting order parameter with point nodes. Millikelvin specific heat
measurements performed on the same crystals used for thermal transport reveal
an upturn below 300 mK that is well described by a divergent quantum-critical
contribution to the density of states (DOS). Modeling this contribution with a
T^{-1/3} power law allows restoration of the full entropy balance in the
superconducting state and a resultant cubic power law for the electronic DOS
below T_c, consistent with the point-node gap structure determined by thermal
conductivity and penetration depth measurements.
