This paper aims to investigate the effect of two-temperature and the Thomson effect in a micropolar thermoelastic medium with the void problem in the context of Green–Naghdi (G–N) theory. The normal mode analysis is used to obtain the analytical expressions of the considered variables. The non-dimensional displacement, temperature, micro-rotation, the change in the volume fraction field, and stress of the material are obtained and illustrated graphically. The variations of these quantities have been depicted graphically in the G–N theories of type-II and III. From numerical calculations, the effects of the Thomson parameter and two-temperature parameter on a homogeneous, isotropic, micropolar thermoelastic material with voids are revealed and discussed. Some particular cases of interest are deduced from the present investigation.