  In this paper, we investigate a thermal coherent state defined with the
Lie-Trotter product formula under the formalism of the thermo field dynamics.
In the definition of our thermal coherent state, we treat the thermalizing
operator and the displacement operator symmetrically. We examine its
uncertainty relation and quasiprobability distributions. Although this thermal
coherent state is equivalent to the conventional ones except for different
parameterizations and a phase factor, it is convenient for describing an
experimental setup of the optical parametric oscillator laser.
