  Motivated by the experimental realization of single-component degenerate
Fermi gases of polar ground state KRb molecules with intrinsic two-body losses
[L. De Marco, G. Valtolina, K. Matsuda, W. G. Tobias, J. P. Covey, and J. Ye, A
degenerate Fermi gas of polar molecules, Science 363, 853 (2019)], this work
studies the finite-temperature loss rate of single-component Fermi gases with
weak interactions. First, we establish a relationship between the two-body loss
rate and the $p$-wave contact. Second, we evaluate the contact of the
homogeneous system in the low-temperature regime using $p$-wave Fermi liquid
theory and in the high-temperature regime using the second-order virial
expansion. Third, conjecturing that there are no phase transitions between the
two temperature regimes, we smoothly interpolate the results to intermediate
temperatures. It is found that the contact is constant at temperatures close to
zero and increases first quadratically with increasing temperature and finally
-- in agreement with the Bethe-Wigner threshold law -- linearly at high
temperatures. Fourth, applying the local-density approximation, we obtain the
loss-rate coefficient for the harmonically trapped system, reproducing the
experimental KRb loss measurements within a unified theoretical framework over
a wide temperature regime without fitting parameters. Our results for the
contact are not only applicable to molecular $p$-wave gases but also to atomic
single-component Fermi gases, such as 40K and 6Li.
