  Thermodynamics of the unitary Fermi gas at finite temperature is investigated
from the perspective of the expansion over epsilon=4-d with d being the
dimensionality of space. We show that the thermodynamics is dominated by
bosonic excitations in the low temperature region T<<Tc. Analytic formulas for
the thermodynamic functions as functions of the temperature are derived to the
lowest order in epsilon in this region. In the high temperature region where T
Tc, bosonic and fermionic quasiparticles are excited. We determine the critical
temperature Tc of the superfluid phase transition and the thermodynamic
functions around Tc to the leading and next-to-leading orders in epsilon.
