Abstract We discuss a model Kondo-type Hamiltonian representing an analytically tractable version of the model used by Yin et.al., Phys. Rev. B 86, 2399 (2012) to explain the non-Fermi liquid behavior of iron chalcogenides and ruthenates in an intermediate energy range. We consider a regime where a complete screening of the local degrees of freedom proceeds in two stages described by two characteristic energy scales T_K^orb >> E_0. The first scale marks a screening of the orbital degrees of freedom and the second one marks a crossover to the regime with coherent propagation of quasiparticles. We present analytical results for the specific heat and magnetic susceptibility at T << T_K^orb.