1995 caprice classic, No warm heat

If it is faulty, yes.
Does the temp gauge show the engine is warming up to normal temp ?
Is the radiator full of coolant ?
Are the heater hoses getting hot ?
It could also be a faulty blend door under the dash. The blend doors direct air thru the heater core and the vents.

Your cooling fan relays are controlled by the Engine Control Module (ECM). What you are unplugging is probably the Engine Coolant Temperature Sensor (ECT). The ECM will default to "fans on" if it loses the circuit to the ECT. (It loses it when you unplug it) This is why the fans come on when you unplug the connector. The engine might be overheating because the ECT may be malfunctioning and "lying" to the computer about what the actual engine temperature is. If this is the case, the ECM is not turning the fans on because it doesn't "think" it is hot enough to need them. Then again, you could have a faulty temperature gauge that is making you think the engine is overheating when it is not. (If it is boiling over, then it is OBVIOUSLY overheating and you can just disregard that last statement.)
Anyway, the only way to properly diagnose the cooling system on your vehicle is to access the live engine data and look to see what temperature the ECM is seing while you take an actual reading with an infrared thermometer or a pyrometer and compare the two. Yhe thermometer or prometer reading should be within about 5 degrees of what the ECM "thinks" the temperature is. If there is a larger error than this then the coolant temp sensor should be replaced. If the reading is within this range and the temperatur gauge reads hot when it is not, then the gauge should be replaced.
Since the fans come on when you unplug the sensor, you know that all the fan circuits are working and the ECM is capable of controlling them, so it almost has to be a computer INPUT problem, not an OUTPUT problem.

Look for a heater control valve under the hood connected to one of the heater hoses and make sure the valve is operating properly. This is what allows the hot water to pass through your heater core. Also your heater core may have a blockage.

Did you run engine from cold, WITH HEATER ON, and fill cap off when re-filling system? If not, try that and see what happens. Let the engine get up to operating temperature and rad fan come on to cool 2 or 3 times before putting cap back on.

Heater core is plugged or you have a air pocket. If you take off the heater lines and try blowing through them both ways. The fans will not move until the engine gets hot.

either a faulty temp sending unit or a thermastat stuck open assuming all wire connections are good. if heater blows hot id lean towards the temp sending unit. please rate me trying to make a buck

first of all I would make sure the car has proper amount of coolant and you are right it is very possible you have an air pocket in the system also ask your self did you change the thermastat after you did the heater core when the car is cold make sure there is coolant at the cold mark on the reservior bottle because you might not have enough coolant then start the car and get it up to temp and if the coolant goes not go up to the hot mark when the car gets to temp you do not have enought coolant just keep adding coolant and you will see the bubble after the thermastat opens

Yes, you re correct! thats a thermostat issue.

what if both hoses are hot. and on idle heat comes on but driving it's blows co

Posible thermastat sticking closed. If thermastat doesn't open heated water is trapped in the engine causing it to run hot and not allowing hot water to travle to the heater core when called for.