Dendrite formation limits the cycle life of lithium and sodium metal anodes and remains a major challenge for their integration into next-generation batteries, even when replacing the liquid electrolyte by a solid electrolyte. Voids forming in solid metal anodes at the interface to a solid electrolyte on stripping cause current constrictions on plating and promote dendrite formation. Recent studies showed that alkali metal creep is the primary mechanism for replenishing the voids at room temperature. Here, we investigate plating and stripping of liquid sodium metal from a carbon-coated ceramic Na-β"-alumina electrolyte at 250 °C, thereby eliminating creep-related mass transport limitations. We demonstrate extremely high current densities of up to 2600 mA/cm² and cumulative plating capacities of >10 Ah/cm² at 1000 mA/cm² without dendrite formation. Our results demonstrate that liquid metal anodes can be paired with solid electrolytes, providing a practical solution to suppress dendrite formation at high current densities.