In this paper we study the equations describing the thermal convection in an incompressible viscous electrically conducting micropolar fluid in the presence of a magnetic field, taking into account the effect of Hall current. The system is a combination of the generalized magnetic induction, the equations of micropolar fluids and the temperature equation. We prove long-time and large-data existence of a weak solution with decreasing energy to the system posed in a bounded domain of R3 and equipped with initial and boundary conditions.