In this Rapid Communication we introduce a thermal magnetotorsional effect (TME) as a topological response in magnetic Weyl semimetals. We predict that magnetization gradients perpendicular to the Weyl node separation give rise to temperature gradients depending only on the local positions of the Weyl nodes. The TME is a consequence of magnetization-induced effective torsional spacetime geometry and the finite-temperature Nieh-Yan anomaly. Similarly to the anomalous Hall effect and chiral anomaly, the TME has a universal material-independent form. We predict that the TME can be observed in the magnetic Weyl semimetal EuCd2As2.