  We present an exhaustive study of the coherent heat transport through
superconductor-ferromagnet(S-F) Josephson junctions including a spin-filter
(I$_{sf}$) tunneling barrier. By using the quasiclassical Keldysh Green's
function technique we derive a general expression for the heat current flowing
through a S/F/I$_{sf}$/F/S junction and analyze the dependence of the thermal
conductance on the spin-filter efficiency, the phase difference between the
superconductors and the magnetization direction of the ferromagnetic layers. In
the case of non-collinear magnetizations we show explicitly the contributions
to the heat current stemming from the singlet and triplet components of the
superconducting condensate. We also demonstrate that the magnetothermal
resistance ratio of a S/F/I$_{sf}$/F/S heat valve can be increased by the
spin-filter effect under suitable conditions.
