Heat pipes continuously transport the latent heat of vaporization from the evaporator to the condenser in the heat pipes due to the capillary pressure created by the menisci in the wick pumping the condensed fluid back to the evaporator. The heat pipe heat transfer capacity is then limited by the capillary limit. However, fewer capillary limit experiments were conducted to investigate the transient temperature variations and physical mechanism at the capillary limit for liquid metal wick heat pipes. This work presents capillary limit transient measurements on a sodium screen-wick heat pipe for high heat fluxes, high heating rates during frozen startup, and negative and positive inclination angles. It also investigates the special behavior before and after dryout, including dryout oscillations and the recovery process to understand the cause and physical mechanism at the capillary limit. The direct cause of the capillary limit is that the evaporation rate exceeds the capillary-driven liquid supply to the evaporator. The experiments show that the capillary limit creates a rapid temperature increase of about 5 °C/s at the evaporator end, while the condenser and adiabatic section temperatures decrease. Dryout oscillations were observed with positive inclinations before the capillary limit. After the capillary limit, reducing the power to just below the limit does not lead to heat pipe recovery, but the power needs to be reduced by about 30% of the critical heat flux to make the heat pipe return to its normal operating state.