  We study theoretically the influence of the temperature and disorder on the
spin wave spectrum of the magnonic crystal Fe$_{1-c}$Co$_{c}$. Our formalism is
based on the analysis of a Heisenberg Hamiltonian by means of the wave vector
and frequency dependent transverse magnetic susceptibility. The exchange
integrals entering the model are obtained from the \emph{ab initio} magnetic
force theorem. The coherent potential approximation is employed to treat the
disorder and random phase approximation in order to account for the softening
of the magnon spectrum at finite temperatures. The alloy turns out to exhibit
many advantageous properties for spintronic applications. Apart from high Curie
temperature, its magnonic bandgap remains stable at elevated temperatures and
is largely unaffected by the disorder. We pay particular attention to the
attenuation of magnons introduced by the alloying. The damping turns out to be
a non-monotonic function of the impurity concentration due to the non-trivial
evolution of the value of exchange integrals with the Co concentration. The
disorder induced damping of magnons is estimated to be much smaller than their
Landau damping.
