This paper theoretically studies the thermo-magnetic loading effects on the long-term (>100 s, reaching the steady state) high-frequency (>100 Hz) dynamic behaviour of magnetic shape memory alloys actuated by cyclic magnetic fields. The material's dynamic behaviour at different levels of ambient heat-transfer, ambient temperature, applied magnetic field frequency and amplitude are simulated by a dynamic model incorporating both magnetic-field-induced martensite reorientation and temperature-driven martensitic phase transformation. Analytical expressions of the material's long-term steady-state behaviour (i.e., stable strain amplitude and temperature) as a function of ambient thermal conditions and magnetic loading conditions are further derived. It is found from model simulations and analytical calculations that weak ambient heat-transfer, high ambient temperature, and high magnetic field amplitude (to trigger martensite reorientation) lead to large net heat generation from dissipative martensite reorientation and thus increase material's stable temperature, which results in reduced twinning stress and increased stable strain amplitude. It is also found that the material's stable temperature can reach the characteristic phase transformation temperature triggering the martensite-to-austenite transformation. In this case, weaker ambient heat transfer, higher ambient temperature and higher magnetic field frequency result in larger heat generation rate accelerating the martensite-to-austenite transformation. Therefore, less martensite remains in the material and the material's stable strain amplitude becomes smaller.