  We report the temperature dependence of the low-temperature specific heat
down to 400 mK of the electron-doped Ba(Fe$_{0.92}$Co$_{0.08}$)$_{2}$As$_{2}$
superconductors. We have measured two samples extracted from the same batch:
first sample has been measured just after preparation with no additional heat
treatment. The sample shows $T_{c}$=20 K, residual specific heat
$\gamma_{0}$=3.6 mJ/mol K$^{2}$ and a Schottky-like contribution at low
temperatures. A second sample has been annealed at 800 $^{o}C$ for two weeks
and shows $T_{c}$ = 25 K and $\gamma_{0}$=1.4 mJ/mol~K$^{2}$. By subtracting
the lattice specific heat, from pure BaFe$_{2}$As$_{2}$, the temperature
dependence of the electronic specific heat has been obtained and studied. For
both samples the temperature dependence of $C_{el}(T)$ clearly indicate the
presence of low-energy excitations in the system. Their specific heat data
cannot be described by single clean s- or d-wave models and the data requires
an anisotropic gap scenario which may or may not have nodes
