The entropy uncertainty relation principle is one of the most fundamental characteristics of quantum information and quantum technology. In this paper, based on the quantum memory-assisted entropy uncertainty relation (QMA-EUR), we study the dynamics of entropy uncertainty for the Heisenberg model of two qubits. A detailed analysis is presented for the effects of Dzyaloshinskii-Moriya (DM) interaction strength D, coupling strength J and temperature T on theentropy uncertainty in both the ferromagnetic (J<0) and antiferromagnetic (J>0) regimes. The numerical result shows that the entropy uncertainty can be reduced by the increase of the interaction strength D or coupling strength J, implying that the measuring outcomes can be predicted more precisely. It is demonstrated that the entropy uncertainty is closely related to the increase of the thermodynamic temperature. It implies that the accuracy of measurement result decreases with the increase of the thermodynamic temperature. Moreover, the effect of DM on the entropy uncertainty of the system in both the ferromagnetic and antiferromagnetic regimes at high temperature or low temperature are discussed respectively. On the one hand, the entropy uncertainty does not approach a constant value in ferromagnetic systems at low temperatures. Besides, in antiferromagnetic systems, the entropy uncertainty is always close to zero at low temperatures, implying that the measuring outcomes can be predicted precisely. As a comparison, in antiferromagnetic systems, the entropy uncertainty is not always close to zero at low temperature. When DM interaction strength D is small, the increase of temperature can improve the entropy uncertainty relation of the system and plays a more significant role in ferromagnetic system. The effective regulation mechanism of the entropy uncertainty of the Heisenberg model is revealed. Moreover, the underlying physics for the dynamical evolution of entropy uncertainty are analyzed by mixedness, where the increase of mixedness is considered to result in the enhancement of uncertainty, and vice versa.