  Bosonization predicts that the specific heat, C(T), of a one-dimensional
interacting Fermi system is a sum of the specific heats of free collective
charge and spin excitations, plus the term with the running backscattering
amplitude which flows to zero logarithmically with decreasing T. We verify
whether this result is reproduced in the g-ology model. Of specific interest
are the anomalous terms in C(T) that depend on the bare backscattering
amplitude. We show that these terms can be incorporated into a renormalized
spin velocity. We do this by proving the equivalence of the results for C(T)
obtained within the g-ology model and by bosonization with velocities obtained
by the numerical solution of the Bethe-ansatz equations for the Hubbard model.
