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Heat transfer in water was visually investigated using a liquid-crystal sheet with thermochromism in a hybrid magnet. Upward thermal convection was significantly suppressed by gradient magnetic fields, however, it remained even under magnetic levitation conditions with a gradient field of B(dB/dz)=-1360 T2 m-1. A thermal conduction state without convection was realized under a stronger gradient field of B(dB/dz)=-2880 T2m-1 at 35-40°C, and surprisingly the downward magnetic convection was observed under the same field at 40-45°C. The temperature dependence of the magnetic susceptibility of water is responsible for the convection behavior in the gradient fields.