Abstract: Based on Ritz transient temperature field functional, the variational solution of temperature field for the plate after rolling during fully developed regime was first obtained by variational method. Its distribution was a parabola. The comparison between the variational results and those analytical results by the separation variable method as well as the numerical results by finite difference method showed that the results obtained by variational method have higher forecast precision with the analytical and numerical results, and the maximum error among them is less than 6°C. Besides, the expressions of the average temperature, average cooling rate, occurrence location of the average temperature, the temperature difference between plate surface and centre along thick direction, and the time required for cooling to a certain margin of error are also given. A test proves the reliability of variational function.