  We present a relativistic quantum mechanics of a point mass with absolute
thermodynamic time and temperature, combined to a single complex parameter of
evolution. In this theory, the geometric time is introduced as one of
space-time coordinates; it does not coincide with the thermodynamic time on the
kinematical level. It is established, that the theory allows a consistent
dynamics with nontrivial probability density at the limit $\hbar\to 0$. We
identify this dynamics with the classical one, and prove its relativistic
invariance. It is shown, that the thermodynamical time becomes proportional to
the proper time of the point mass in the conventional classical regime of its
evolution with the delta-functional distribution of the probability density.
