  We present self-consistent calculations of the multi-gap structure measured
in some Fe-based superconductors. These materials are known to have structural
disorder in real space and a multi-gap structure due to the $3d$ Fe-orbitals
contributing to a complex Fermi surface topology with hole and electron
pockets. Different experiments identify three s-wave like superconducting gaps
with a single critical temperature ($T_c$). We investigate the temperature
dependence of these gaps by a multi-band Bogoliubov-deGennes theory at
different pockets in the presence of effective hybridizations between some
bands and an attractive temperature dependent intra-band interaction. We show
that this approach reproduces the three observed gaps and single $T_c$ in
different compounds of Ba$_{1-x}$K$_{x}$Fe$_2$As$_2$, providing some insights
on the inter-band interactions.
