  We investigate the intrinsic anomalous thermal Hall effect as an effective
probe of the order parameters of non-unitary pairing states of the putative
spin-triplet superconductor UTe$_2$. We consider all symmetry-allowed
non-unitary states under magnetic fields comprehensively, and calculate the
anomalous Hall conductivity arising from time-reversal symmetry-breaking Weyl
point nodes of the gap functions, assuming three types of Fermi surfaces;
ellipsoid-shaped, cylinder-shaped, and ring-shaped ones, which are predicted by
previous band calculations. We find the nonzero anomalous thermal Hall
conductivity in the certain ratio of the two irreducible representations. The
results may be utilized for future exploration of pairing states of UTe$_2$.
