Implementing the IIoT concept in industry involves the development and implementation of online systems monitoring the technical state of electromechanical equipment. This is achieved through the use of digital twins and digital shadows (object state observers). The tasks of mastering new rolling profiles and optimizing plate mill rolling programs require improved methods for calculating equivalent motor currents and torques. Known methods are generally based on calculations using smoothed load diagrams, which are assumed to be identical for the upper and lower main drive (UMD and LMD) rolls. These methods do not consider the differences in actual loads (currents or torques) in steady rolling states. Experiments performed on the 5000 plate mill have shown that due to speed mismatches, the UMD and LMD torques differ three times or more. This causes overheating of the more heavily loaded motor, insulation life reduction, and premature failure. Therefore, the problem of developing and implementing techniques for monitoring the load and thermal regimes of motors using digital observers is relevant. The paper’s contribution is the first justification of the concept of object-oriented digital shadows. They are developed for specific classes of industrial units using open-source software. This research justifies a methodology for assessing motor load and temperature by processing arrays of motor currents or torques generated during rolling. An equivalent load observer and a temperature observer were proposed and implemented using Matlab-Simulink resources. The algorithm was implemented on the mill 5000 and tuned using an earlier-developed virtual commissioning methodology with digital twins. Thermal regimes were studied, proving that torque alignment ensures equal motor temperatures. The proposed considerations contribute to the development of the theory and practice for creating digital systems to monitor the technical condition of electromechanical and mechatronic systems and implementing the Industry 4.0 concept at industrial enterprises.