To date, the choice of the geometry of a magnetic cooling cell is a relevant problem in the field of magnetic refrigeration. In this study, the heat transfer processes in three-dimensional magnetic cooling cells containing Fe–Rh microwires are studied within the theoretical simulation approaches. The velocities of heat carrier flow velocities of 2.5 and 0.7 m/s are considered. It is found that the relaxation times are 0.8 and 1.4 ms for a flow velocity of 2.5 m/s, and 1.8 and 3.3 ms for a flow velocity of 0.7 m/s in the case of using microwire diameters of 10 and 50 µm, respectively. It is shown that the use of Fe–Rh microwires in magnetic cooling cells can be promising for magnetic refrigeration technology.