In the present Rapid Communication we calculate the density matrix of heat conduction based on the field theory of nonequilibrium thermodynamics, which was worked out in the last 10 years. Applying these results we can discuss the existence of the maximal temperature and a possible upper limit for its value. We point out, proposing relevant physical assumptions, that this temperature could be the so-called Planck temperature [J. A. S. Lima and M. Trodden, Phys. Rev. D 53, 4280 (1996)].