A Mach-Zehnder (M-Z) interferometer is applied to study the temperature field in a fluid at a periodically magnetized gadolinium (Gd) plate during magnetization stage. N-decane is used for the reference case, pure thermal diffusion, because of its high refractive index change with temperature. In a second class of experiments, a 0.5 M NaOH solution is used as heat transfer fluid. By means of injecting an electric current ranging from 1 mA to 3 mA into the alkaline solution during the magnetization stage, a magnetohydrodynamic flow is generated. We find that this flow provides an enhancement of the energy exchange between the Gd plate and the fluid which is about 30% for a Reynold number of ca. 15.3. Besides, the enhancement is increased quasi-linearly with the Reynold number in present setup.