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We show that the projected Gross-Pitaevskii equation (PGPE) can be mappedexactly onto Hamilton's equations of motion for classical position and momentumvariables. Making use of this mapping, we adapt techniques developed instatistical mechanics to calculate the temperature and chemical potential of aclassical Bose field in the microcanonical ensemble. We apply the method tosimulations of the PGPE, which can be used to represent the highly occupiedmodes of Bose condensed gases at finite temperature. The method is rigorous,valid beyond the realms of perturbation theory, and agrees with an earliermethod of temperature measurement for the same system. Using this method weshow that the critical temperature for condensation in a homogeneous Bose gason a lattice with a UV cutoff increases with the interaction strength. Wediscuss how to determine the temperature shift for the Bose gas in thecontinuum limit using this type of calculation, and obtain a result inagreement with more sophisticated Monte Carlo simulations. We also consider thebehaviour of the specific heat.Comment: v1: 9 pages, 5 figures, revtex 4. v2: additional text in response to  referee's comments, now 11 pages, to appear in Phys. Rev.

Microcanonical temperature for a classical field: Application to Bose-Einstein condensation