  We investigate the strongly interacting hard-core anyon gases in a one
dimensional harmonic potential at finite temperature by extending thermal
Bose-Fermi mapping method to thermal anyon-ferimon mapping method. With thermal
anyon-fermion mapping method we obtain the reduced one-body density matrix and
therefore the momentum distribution for different statistical parameters and
temperatures. At low temperature hard-core anyon gases exhibit the similar
properties as those of ground state, which interpolate between Bose-like and
Fermi-like continuously with the evolution of statistical properties. At high
temperature hard-core anyon gases of different statistical properties display
the same reduced one-body density matrix and momentum distribution as those of
spin-polarized fermions. The Tan's contact of hard-core anyon gas at finite
temperature is also evaluated, which take the simple relation with that of
Tonks-Girardeau gas $C_b$ as $C=\frac12(1-cos\chi\pi)C_b$.
