The generalized magneto-thermoelastic problem of an infinite homogeneous isotropic microstretch half-space with temperature-dependent material properties placed in a transverse magnetic field is investigated in the context of different generalized thermoelastic theories. The upper surface of the half-space is subjected to a zonal time-dependent heat shock. By solving finite element governing equations, the solution to the problem is obtained, from which the transient magneto-thermoelastic responses, including temperature, stresses, displacements, microstretch, microrotation, induced magnetic field and induced electric field are presented graphically. Comparisons are made in the results obtained under different generalized thermoelastic theories to show some unique features of generalized thermoelasticity, and comparisons are made in the results obtained under three forms of temperature dependent material properties (absolute temperature dependent, reference temperature dependent and temperature-independent) to show the effects of absolute temperature and reference temperature. Weibull or Log-normal.