My car is an 01 deville base. It has been running perfectly, except I had a noisy pulley making a constant screeching sound. I had an appointment to get it looked at Friday. I stopped in at my mothers house left the car idling outside for 10 mins, and when I came out the screeching had stopped. But when I got in the car the temp gauge was up, and the fans were on. It continued to get hotter so I shut it down. The belt is still there, I'm not missing any coolant, and it never overflowed and there is no smell of coolant. Is it possible for the waterpump to fail internally?