  In the present paper we investigate the Tonks-Girardeau gas confined in a
harmonic trap at finite temperature with thermal Bose-Fermi mapping method. The
pair distribution, density distribution, reduced one-body density matrix, the
occupations number of natural orbitals, and momentum distribution are
evaluated. In the whole temperature regime the pair distribution and density
distribution exhibit the same properties as those of polarized free Fermions
because both of them depend on the modulus of wavefunction rather than
wavefunction. While the reduced one-body density matrix, the natural orbital
occupation, momentum distribution, which depend on wavefunction, of Tonks gas
displays Bose properties different from polarized free Fermions at low
temperature. At high temperature we can not distinguish Tonks gas from the
polarized free Fermi gas by all properties qualitatively.
