Replaced radiator (due to small leak), hoses and thermostat (thought thermostat was stuck open). Temp gage needle stays under cold. When the needle finally gets to the cold mark I turn on the heat and it will give me heat for 3-6 sec and again drop to under cold. Needle will not go pass the cold mark no matter how long I am driving. Fan constantly stays on.

Did you try unplugging the fan and see if it warms up? Have you tried blocking the face of the radiator with cardboard and see if it warms up? Are you sure all your hoses are routed properly ?

Something is definitely very wrong. Be extremely careful not to drive long distances before taking the car to a mechanic.

It sounds as though the coolant is not circulating properly. The heater in the car is dependent on the heat from the coolant. And the temp gauge is probably measuring coolant temperature. But the fan is probably reading from a different sensor and knows that the engine is running hot.

I would have the cooling fan system tested and I may also recommend another thermostat from another source (in case the replacement is faulty... remember "NEW" stands for Never Ever Worked... )

I had a 99 Ranger with the V-6 in it and it had an old style mechanical fan with a fan clutch on it. It was doing the same thing. The fan clutch was bad and that was causing the fan to constantly be spinning which wouldn't allow the engine to really ever get warm. I replaced the fan clutch and that solved the problem.