Magnetic microrobots (MMs) have been receiving tremendous attention due to their advantages of untethered controllability and biocompatibility, and they have been shown to be promising tools for targeted therapy. Ahead of implementations, one of the most vital motion properties of the MMs, i.e., the fundamental spin motility should be characterized for better utilization. To fulfill the precise characterization of MMs, it is of great value to develop an electromagnetic field generator with high accuracy. One electromagnetic field generator usually equips its coils with iron cores to enhance the generated magnetic field (MF) strength, which may also bring in unwanted nonlinear and temperature-dependent dynamic properties. The complex properties usually make the coils hard to control to maintain consistent good performances. To generate a desirable MF under varying temperature conditions, this study develops a model prediction adaptive control (MPAC) approach to regulate the coil system adaptively. Validation tests show that, compared with the prevalent MPC method, the MPAC approach can generate a more accurate MF at different ambient temperatures. As an application, the MPAC-controlled MF generator is utilized to characterize the MM's spin motility, and a nonlinear dynamic model is established, which can properly describe the MM's spin behavior under various excitation conditions.