Disclosed are a continuous temperature measuring device used in a Ruhrstahl-Heraeus (RH) process of performing vacuum degassing among steel making processes in an ironworks and an RH apparatus including the same. The RH apparatus includes a sensor hole formed at a lower vessel of a vacuum vessel; a continuous temperature measuring device mounted on the sensor hole and including a light-to-temperature converter measuring temperature based on received light, a light guide rod receiving light from a measurement target, an optical fiber transferring the light received by the light guide rod to the light-to-temperature converter, a connector connecting the optical fiber to the light guide rod while maintaining straightness of the optical fiber, a primary protection tube enclosing an outer peripheral surface of the light guide rod, a flexible heat resistant tube protecting the optical fiber, and a joint connected to the flexible heat resistant tube and provided with a cooling gas injection tube; and a cooling gas supply unit supplying cooling gas to the cooling gas injection tube.