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Thermodynamics of the XXX Heisenberg model is studied. The trace of theBoltzmann weight with respect to the Hilbert space is taken in thethermodynamic limit with the number of up-spins being fixed. The expression ofthe trace gives an explanation why the correct thermodynamic quantities arederived from the string hypothesis. Combining this with the previous result, weconclude that the free energy can be calculated only by assuming the Betheansatz equation. The method is more direct than other known methods which wereused to derive the free energy.Comment: 52 pages, submitted to J. Math. Phy

A direct calculation of the free energy from the Bethe ansatz equation for the Heisenberg model