A smart beam made of magneto-electro-elastic (MEE) material having piezoelectric phase and piezomagnetic phase, shows the coupling between magnetic, electric, thermal and mechanical under thermal environment. Product properties such as pyroelectric and pyromagnetic are generated in this MEE material under thermal environment. Recently studies have been published on the product properties (pyroelectric and pyromagnetic) for magneto-electro-thermo-elastic smart composite. Hence, the magneto-electro-elastic beam with different volume fractions, investigated under uniform temperature rise is the main aim of this paper, to study the influence of product properties on clamped-free boundary condition, using finite element procedures. The finite element beam is modeled using eight node 3D brick element with five nodal degrees of freedom viz. displacements in the x, y and z directions and electric and magnetic potentials. It is found that a significant increase in electric potential observed at volume fraction of $BaTiO_3$, $v_f$ = 0.2 due to pyroelectric effect. In-contrast, the displacements and stresses are not much affected.