  We predict the thermal counterpart of the anomalous Josephson effect in
superconductor/ferromagnet/superconductor junctions with non-coplanar magnetic
texture. The heat current through the junction is shown to have the
phase-sensitive interference component proportional to $\cos(\theta -
\theta_0)$, where $\theta$ is the Josephson phase difference and $\theta_0$ is
the texture-dependent phase shift. In the generic tri-layer magnetic structure
with the spin-filtering tunnel barrier $\theta_0$ is determined by the spin
chirality of magnetic configuration and can be considered as the direct
manifestation of the energy transport with participation of spin-triplet Cooper
pairs. In case of the ideal spin filter the phase shift is shown to be robust
against spin relaxation caused by the spin-orbital scattering. Possible
applications of the coupling between heat flow and magnetic precession are
discussed.
