  We have studied the vacuum and thermal fluctuation energies of a soliton at
finite temperatures. First the vacuum energy coming from the Dirac sea is
calculated by a summation of the discrete and continuum energy spectrum of the
Dirac equation in the background field of a soliton. And all the divergences
are removed by the same renormalization scheme at zero temperature. Then the
vacuum energy and thermal fluctuation energy at finite temperatures in a
temperature dependent soliton background are calculated. And the numerical
results are analyzed and discussed.
