  On the basis of Bethe ansatz solution of one dimensional SU(4) Hubbard-like
model, we study its thermodynamics properties by means of Yang-Yang
thermodynamics Bethe ansatz. The Land\'e $g$ factor is taken into account so as
to describe electrons with orbital degeneracy. The free energy at low
temperature is given and the specific heat both in strong coupling and weak
coupling limits are obtained.
