  The Nambu--Jona-Lasinio model is widely used to study strong-interaction
phenomena in vacuum and quark matter. Since the model is nonrenormalizable, one
needs to work within a specific regularization scheme to obtain finite results.
Here we show that a commonly used cutoff regularization scheme leads to
unphysical results, such as superluminal speed of sound and wrong
high-temperature behavior of the specific heat and other thermodynamical
quantities. Such a troublesome feature of the cutoff regularization invalidates
the model for temperature and baryon density values relevant to the
phenomenology of heavy-ion collisions and compact stars. We show that the
source of the problems stems from cutting off momentum modes in finite
integrals depending on thermal distribution functions in the grand canonical
potential. The problems go away when taking into account the full momentum
range of those integrals. Explicit examples are worked out in the SU(2)-flavor
version of the model.
