The Landau Pole at Finite Temperature

We study the Landau pole in the lambda phi^4 field theory at non-zero and large temperatures. We show that the position of the thermal Landau pole Lambda_L(T) is shifted to higher energies with respect to the zero temperature Landau pole Lambda_L(0). We find for high temperatures T > Lambda_L(0), Lambda_L(T) simeq pi^2 T / log (T / Lambda_L(0)). Therefore, the range of applicability in energy of the lambda phi^4 field theory increases with the temperature.