  The heat coefficients related to the Laplace-Beltrami operator defined on the
hyperbolic compact manifold $H^3/\Ga$ are evaluated in the case in which the
discrete group $\Ga$ contains elliptic and hyperbolic elements. It is shown
that while hyperbolic elements give only exponentially vanishing corrections to
the trace of the heat kernel, elliptic elements modify all coefficients of the
asymptotic expansion, but the Weyl term, which remains unchanged. Some physical
consequences are briefly discussed in the examples.
