Approaches for creating magnetically controlled thermal accumulators for aerospace engineering based on thermomagnetic convection under the action of a magnetic field created by neodymium magnet under thermal conditions are discussed. The properties of thermal accumulating material (TM) containing magnetic particles are studied. To investigate the distribution of the temperature field it was used a contactless measurement method realized using a thermal imager. The formulation of the problem of mathematical modeling for a thermal control system with TM based on the finite integral transform method is carried out. It allows to study the distribution of temperature fields at design stage. The application of the effect of thermomagnetic convection makes it possible to intensify heat exchange in TM, which increases the efficiency of charge and discharge of TM. This approach is economically feasible and technologically adapted to aerospace technology. © Published under licence by IOP Publishing Ltd.