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The method of the effective action for the composite operators $\Phi^2(x)$and $\Phi^4(x)$ is applied to the termodynamics of the scalar quantum fieldwith $\lambda\Phi^4$ interaction. An expansion of the finite temperatureeffective potential in powers of $\hbar$ provides successive approximations tothe free energy with an effective mass and an effective coupling determined bythe gap equations. The numerical results are studied in the space-time of onedimension, when the theory is equivalent to the quantum mechanics of ananharmonic oscillator. The approximations to the free energy show quickconvergence to the exact result.Comment: 10 pages, plain Latex, 2 figure

The Finite Temperature Effective Potential for Local Composite Operators