Devices capable of actively controlling heat flow have been desired by the thermal management community for decades. The need for thermal control has become particularly urgent with power densification resulting in devices with localized heat fluxes as high as 1 kW/cm2. Thermal switches, capable of modulating between high and low thermal conductances, enable the partitioning and active control of heat flow pathways. This paper reports a millimeter-scale thermal switch with a switching ratio >70, at heat fluxes near 10 W/cm2. The device consists of a silicone channel filled with a reducing liquid or vapor and an immersed liquid metal Galinstan slug. Galinstan has a relatively high thermal conductivity (≈16.5 W/mK at room temperature), and its position can be manipulated within the fluid channel, using either hydrostatic pressure or electric fields. When Galinstan bridges the hot and cold reservoirs (the “ON” state), heat flows across the channel. When the hot and cold reservoirs are instead filled with the encapsulating liquid or vapor (the “OFF” state), the cross-channel heat flow significantly reduces due to the lower thermal conductivity of the solution (≈0.03–0.6 W/mK). We demonstrate switching ratios as high as 15.6 for liquid filled channels and 71.3 for vapor filled channels. This work provides a framework for the development of millimeter-scale thermal switches and diodes capable of spatial and temporal control of heat flows.