In an antiferromagnet (AF) with uniaxial anisotropy, spin-up and spin-down magnons coexist and form an intrinsic degree of freedom resembling electrons. When polarized by an adjacent ferromagnet (F), a magnonic pure spin current can be thermally generated in an AF. We explore thermal magnon transport in an insulating F/AF/F trilayer where propagating magnons inside the AF spacer can transfer angular momenta between the two Fs. We find that a sufficiently large temperature gradient can switch the downstream F via a magnonic spin-transfer torque if it is initially antiparallel with the upstream F. A reciprocal switching is achievable by reversing the temperature gradient. In typical materials, we estimate the threshold to be 1 K/nm at room temperature, which can be reduced by enhancing the interfacial exchange coupling and by increasing the temperature.