  We have developed a new method for evaluating the specific heat of lattice
spin systems. It is based on the knowledge of high-temperature series
expansions, the total entropy of the system and the low-temperature expected
behavior of the specific heat as well as the ground-state energy. By the choice
of an appropriate variable (entropy as a function of energy), a stable
interpolation scheme between low and high temperature is performed. Contrary to
previous methods, the constraint that the total entropy is log(2S+1) for a spin
S on each site is automatically satisfied. We present some applications to
quantum spin models on one- and two- dimensional lattices. Remarkably, in most
cases, a good accuracy is obtained down to zero temperature.
