Three-terminal thermal analogies to electrical transistors have been proposed for use in thermal amplification, thermal switching, or thermal logic, but have not yet been demonstrated experimentally. Here, we design and fabricate a three-terminal magnetic thermal transistor in which the gate temperature controls the source-drain heat flow by toggling the source-drain thermal conductance from ON to OFF. The centimeter-scale thermal transistor uses gate-temperature dependent magnetic forces to actuate motion of a thermally conducting shuttle, providing thermal contact between source and drain in the ON state while breaking contact in the OFF state. We measure source-drain thermal switch ratios of 109 ± 44 in high vacuum with gate switching temperatures near 25 °C. Thermal measurements show that small heat flows into the gate can be used to drive larger heat flows from source to drain, and that the switching is reversible over >150 cycles. Proof-of-concept thermal circuit demonstrations show that magnetic thermal transistors can enable passive or active heat flow routing or can be combined to create Boolean thermal logic gates. This work will allow thermal researchers to explore the behavior of nonlinear thermal circuits using three-terminal transistors and will motivate further research developing thermal transistors for advanced thermal control.