None of the hoses will get hot, engine will overheat but the temp gauge will not necessarily move.(It depends where the sensor is). There will be no way for the water to move around the system. If there is doubt I wouldn`t use the car until a new one is fitted
If all other hoses are hot and gauge is working then my first steps would be either air lock (has any work been done lately or any leaks?), if all else is hot I would think the pump is moving the water.
Next step for me would be headgasket. Are the hoses getting pressurised quickly?