We study the superconductor/ferromagnet/superconductor junction with non-coplanar magnetic texture under the applied temperature bias. 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 heat 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.