The set of differential equations for an multicore fiber amplifier with pump, signal and the first-order Stokes, taking into account effects of thermal gradient caused by heat generation, is presented. The thermal conduction equations are solved by finite element method. The influence of pump schemes, pump power, convective coefficient, initial power of Stokes, density of the rare earth dopant and fiber length on suppression of the stimulated Brillouin scattering is studied. The results show that the backward pump scheme has advantage over the forward pump scheme in suppression of stimulated Brillouin scattering. Increasing density of the rare earth dopant can lead to higher slope efficiency and shorter optimal fiber length, which can further suppress stimulated Brillouin scattering. The stimulated Brillouin scattering gain and maximum operating temperature are compared between single core fiber amplifier and 19-core fiber amplifier with the same optimal fiber length. Compared with the single core fiber amplifier, the 19-core fiber amplifier has lower maximum operating temperature, which provides more space for further increase in output power.