This work reports the longitudinal thermal conductivity, κ, of Ag- and Cu/Ag-sheathed Ba 1-x K x Fe 2 As 2 conductors. Our investigation has been carried out between 4 K and 80 K with magnetic fields up to 19 T. In the case of Ag-sheathed tapes, the thermal conductivity reaches maximum values of ~80 Wm -1 K -1 and is weakly dependent on the field. The use of Cu/Ag in the place of Ag allows increasing κ up to ~250 Wm -1 K -1 . Zero-field κ values are about one order of magnitude lower than those achieved in other technical superconductors that employ a silver matrix, as Bi 2 Sr 2 CaCu 2 O 8+x (Bi2212) and Bi 2-x Pb x Sr 2 Ca 2 Cu 3 O 10-x (Bi2223). This is a consequence of the contamination of the metal sheaths because of elemental diffusion occurring during the tape sintering. The differences in κ between the Ba 1-x K x Fe 2 As 2 tapes and the other technical superconductors with an Ag matrix become smaller at high field. We suggest that performing the sintering at high pressure could represent a way to reduce the elemental contamination and thus improving the thermal conductivity.