The present work attempts to investigate the influence of the Thomson heating and the Fourier’s heat conduction, in the presence of a magnetic field, on half-space thermoelectricity solid with voids. The material is heated by a non-Gaussian laser beam with pulse duration of 0.23 ps. The heat conduction equation is affected by the Thomson coefficient. A constant Thomson coefficient, instead of traditionally a constant Seebeck coefficient, was assumed. The charge density of the induced electric current is taken as a function of time. The basic governing equations are modified by using Green–Naghdi theory of type-III. A normal mode method is proposed to analyze the problem and obtain numerical solutions. The results of the physical quantities have been illustrated graphically by a comparison between two values of time, with and without void parameters, as well as with and without Thomson coefficient.