Understanding and controlling heat flow in low-dimensional magnetic materials is central to thermoelectrics and spin caloritronics. One of the challenges is the absence of sensitive probes of small, field-dependent modulations in thermal transport. Here we demonstrate transverse Seebeck thermometry using exfoliated TaIrTe₄ as a probe of thermal conductivity modulated by an external magnetic field on a van der Waals magnet, CrPS₄. With a temperature gradient oriented at 45^∘ to its principal crystallographic axes, TaIrTe₄ exhibits a transverse thermopower exceeding 200 μ V K⁻¹ for 900 nm wide and 30 μm long electrodes, enabling precise detection of variations in the local temperature gradients. Exploiting this with CrPS₄ in a nonlocal geometry, we resolve distinct field dependent thermal conductivity changes associated with both the spin-flip and spin-flop magnetic transitions which we attribute to variations in the magnon-phonon coupling in CrPS₄. At 5 K, the transverse Seebeck response is modulated by more than 8% by an external magnetic field, demonstrating strong magnetic control of heat transport in CrPS₄. This all van der Waals platform offers high sensitivity to modulations of thermal conductivity and a broad adaptability to a wide range of exfoliated magnetic systems.