In recent years, there has been a growing interest in hard-magnetic soft materials (HMSMs) due to their capacity to retain high residual magnetization and undergo significant deformation when subjected to external magnetic loading. The performance of these materials in dynamic actuation modes is substantially affected by temperature. This article introduces a theoretical framework for modeling the dynamic behavior of hard-magnetic soft materials. The neo-Hookean material model is employed to account for the thermal properties of the HSM materials. The governing equation for dynamic motion is derived using Euler-Lagrange's principle for nonconservative systems, allowing the characterization of nonlinear oscillations under both constant and periodic magnetic fluxes. Dynamic stability, resonance properties, dynamic response, and periodicity are characterized using frequency response spectra, time history graphs, phase-plane diagrams, and Poincaré maps. The investigation seeks to comprehend the transition from periodic to quasi-periodic oscillation behavior of actuators. These findings represent an initial step towards designing and developing remotely controlled actuators for various futuristic applications.