The Coulomb glass, a model of interacting localized electrons in a random potential, exhibits a soft gap, the Coulomb gap, in the single-particle density of states (DOS) g(ε,T) close to the chemical potential µ. In this paper we investigate the Coulomb gap at finite temperatures T by means of a Monte Carlo method. We find that the Coulomb gap fills with increasing temperature. In contrast to previous results the temperature dependence is, however, much stronger than g(µ,T)~TD-1 as predicted analytically. It can be described by power laws with the exponents 1.75 ± 0.1 for the two-dimensional model and 2.7 ± 0.1 for the three-dimensional model. Nevertheless, the relation g(µ,T)~g(ε,T=0) with |ε - µ| = kBT seems to be valid, since energy dependence of the DOS at low temperatures has also been found to follow power laws with these exponents.