  We review the problem of divergences in one--loop thermodynamical quantities
for matter fields in thermal equilibrium on a black hole background. We discuss
a number of results obtained for various thermodynamical quantities. Then we
discuss the ansatz called ``literal interpretation" of zeroth law of black hole
mechanics and try to explain the diseases of the conical defect procedure in
light of this ansatz. Finally, an analysis of the consequences implied by our
ansatz on the calculation of the partition function is made.
