  We point out that using the heat kernel on a cone to compute the first
quantum correction to the entropy of Rindler space does not yield the correct
temperature dependence. In order to obtain the physics at arbitrary temperature
one must compute the heat kernel in a geometry with different topology (without
a conical singularity). This is done in two ways, which are shown to agree with
computations performed by other methods. Also, we discuss the ambiguities in
the regularization procedure.
