Q: Overheating/no leaks

Hello. If the cooling system is not leaking, then the engine is consuming the coolant. This is usually attributed to a faulty head gasket. Does the oil have any signs of coolant or water in it? It will look like a milk film or foam on the dip stick or when you drain the oil. If coolant is accumulating on the radiator it is spraying or dripping onto it from somewhere. It may be a leak on a hose, but if it is draining as quickly as it seems, then you would notice it. Have you run the vehicle in park with the hood opened and watched for a spray or leak anywhere? Start by checking the oil for coolant/water contamination. Then proceed to run the car and look for any visual signs of a leak. Only further testing will tell.