Over heating 96 Mercury Sable DS

My battery went out & I replaced it....Since then my car overheats replaced thermostat, gas cap & overflow cap hasn't changed anything. My heater works well. My transmission shifts really hard when the car is overheating doesn't spray water out the reservoir just registers hot, idols high & shifts hard. Any ideas why?

Some of those year engines have a water pump that the fins in the pump literally disintegrate to nothing or next to nothing, thus don't circulate any coolant. That would be my first suspicion.