  We study the low frequency admittance of a small metallic island coupled to a
gate electrode and to a massive reservoir via a \emph{multi channel} tunnel
junction. The ac current is caused by a slowly oscillating gate voltage. We
focus on the regime of inelastic cotunneling in which the dissipation of energy
(the real part of the admittance) is determined by two-electron tunneling with
creation of electron-hole pairs on the island. We demonstrate that at finite
temperatures but low frequencies the energy dissipation is ohmic whereas at
zero temperature it is super-ohmic. We find that (i) the charge relaxation
resistance (extracted from the real part of the admittance) is strongly
temperature dependent, (ii) the imaginary and real parts of the admittance do
not satisfy the Korringa-Shiba relation. At zero temperature the charge
relaxation resistance vanishes in agreement with the recent zero temperature
analysis [M. Filippone and C. Mora, Phys. Rev. B {\bf 86}, 125311 (2012) and P.
Dutt, T. L. Schmidt, C. Mora, and K. Le Hur, Phys. Rev. B {\bf 87}, 155134
(2013)].
