  We report on measurements of the specific heat of the recently discovered
superconductor MgB$_2$ in the temperature range between 3 and 220 K. Based on a
modified Debye-Einstein model, we have achieved a rather accurate account of
the lattice contribution to the specific heat, which allows us to separate the
electronic contribution from the total measured specific heat. From our result
for the electronic specific heat, we estimate the electron-phonon coupling
constant $\lambda$ to be of the order of 2, significantly enhanced compared to
common weak-coupling values $\leq 0.4$. Our data also indicate that the
electronic specific heat in the superconducting state of MgB$_2$ can be
accounted for by a conventional, s-wave type BCS-model.
