Abstract: From the heat conduction, differential equations and definite conditions, a trial function which satisfies boundary condition in advance is set. With the Lagrange multiplier method, the generalized expression of Ritz temperature field functional is first established. The variational solution of temperature field for a plate after rolling during fully developed regime is then first obtained by functional variation. It is a function of plate thick δ, heat transfer coefficient α, specific heat c_p, cooling time t, thermal conductivity λ, plate density ρ, starting cooling temperature T₀, and water temperature T_f. The comparison between the variational results and those analytical results by the separation variable method shows that the present results have high forecast precision and the maximum error between them is no more than 7%. It is also deduced that the average temperature occurs at the location of x=0.577δ, and the temperature difference between plate surface and centre along the thick direction decreases as the cooling time increases. The method in the present paper has not been reported yet.