When I turn on the heating system of the car not work is not sending hot air inside the car.

You might have a faulty water valve. The hot air in the car is supplied by the engine cooling system. As the engine works, it heats up and water is circulated through the system and kept at a cooling level by the radiator. However, this water is still hot, and by turning on the heat in the car, a valve is opened that allows the hot water to circulate through the heater core inside the car.
This core is in fact just a mini radiator, and air from the blower fan inside the car blows air through this mini radiator, thus supplying hot air in the car.
If you don't want hot air in the car, the heater control operates a valve that shuts off the hot water from the engine. If this valve is faulty, it will allow hot water to circulate through the system. Another possibility is that the cable operating the water valve might be maladjusted or the cable or the lever operating the cable is broken or faulty. It often happens that the outer part of the cables slip and the controls operate so-so but never well.
If the cables to the dashboard controls are not adjusted properly or have started slipping, it could also cause the fresh air vent to not close properly, and this will cause a flow of air even when the controls and the fan are turned to the off position.
You can remove the control panel from the dash and check the cables and controls, but it is a finicky job. Maybe you want to take the car to a mechanic?

the heater core may have gone bad or is cloged. if you can find the return line of the core pull off the hose and see if any thing comes out

The antifreeze goes into the cooling system through the cap the same way you'd fill the system during normal car maintenance. You may have another issue as well. There is usually a vacuum or electrically operated shut off valve in line in the heater hoses. Its typically located on the passenger's side close to the firewall under the hood. Its purpose is to keep hot antifreeze from flowing into the heater core when the air conditioning is on. If this valve, a temp sending unit that works in conjunction with this valve or the climate control or a break in the electrical circuit or vacuum line or valve isn't working properly, the symptoms that you describe could and likely would arise. You can usually move this valve open or closed manually to test. Check and repair or replace accordingly if low antifreeze doesn't rectify the problem. Good luck!

I can't speak to your specific car, but in general auto heating systems, it could be a number of other things:

1. The control unit might not be sending the correct signal to the valve that controls the flow of hot water into the core. There is usually a solenoid type valve in the heater hose line that opens when you switch the heat on. If you can get to that valve (if your car has one) you should check that it gets 12VDC when the heat is turned on. A simple way to check that it is opening is to feel the hoses on the passenger compartment side of the valve. If they get too hot to touch when heat is called for, that is probably operating correctly.

2. The car's interior temperature sensor might be bad. These sensors are usually located behind a small grill somewhere on the dash. Some systems actually detect the temperature inside the passenger compartment and they send a signal to the controller that tells that control valve how much to open or close.

3. Some systems actually control the temperature by positioning those vent flaps you are looking to find. On those systems, the hot coolant is sent through the core all the time, and the way the temperature is varied inside is by controlling how open/shut that flap is.

The bottom line is that you need to figure out which way your specific car is supposed to work, and then you can start troubleshooting. I suggest doing internet searches - there are usually forums for car repair - often by make and model. Good luck.

yer crapping us right

cold car = cold air the car generates heat you get heat it's just that simple

try turning the blower down, if you have the fan on full you will feel cooler air from time to time. as the thermostat only measures the ambient tempreture inside the car when this level is met then it will turn off the heat so it will only blow the air from the car which will feel cooler.
if the car is still cold suspect the tempreture control in the car maybe faulty or the water level in the system maybe low.

If you have good heat on one side, it can't possibly be the the thermostat. Good heat on one side means that there is plenty of hot water (water and antifreeze mix) circulating through your heater core. The thermostat controls the temperature of the water. If you have hot water, the thermostat is not at fault. Your Impala is equipped with what is called "zoned climate control". All the inside air (both sides) is still heated by the same heater core. The difference between a "zoned" system and a conventional system is that there is more than one "blend-air" door insided your HVAC housing. The blend-air door swings back and forth to direct the incoming air either through the heater core (for hot air) or around the heater core (for cold air) The drivers blend-air door may be broken or the motor that moves the blend-air door is malfunctioning.

Almost every car(including yours) has a flow through ventilation system which means even with the air turned off air will still come through the vents. Its hot because of outside temp and engine temp. 
Basically just push the recirculation button and it will stop.

Help is HERE!
It looks like an Air lock scenario!
Park vehicle on level ground, when cold remove coolant filler cap, start engine and leave to idle, turn heater to hot blower on full. When at operating temp keep clear of coolant filler area and listen, hopefully gurgling then a boil over, wait and then top up with very warm water/coolant let settle it may boil over again whilst air is still in system.
Check for heat inside car, if hot and coolant settled replace cap but keep an eye on temp gauge for a while as air lock may still be further along cooling system.
Please press the Blue button if sorted!
Paul 'W' U.K.

AC works as so..

It does not actually cool the air, however it removes the heat from it (and without heat the air feels cool). As the air is blown around the car the AC system removes the heat from the air, and then it moves it to the condenser at the front of the car (infront of the radiator).

Now usually the car is moving forward, so that air flow will cool the condenser and then you can move more heat from the air inside the car and push it out the front of the car again. This is why, if you have a front wheel drive car, you will hear the cars fan start as soon as you turn the AC on.

Also the car will be much better at cooling the air that is recirculating inside the car (your a/c system will have a button for this) then if it tries to cool hot air from outside.

The long and short of it is that if you hop in a hot car, start the car and run the ac (even at full) it wont be cool straight away, it is mostly influenced by how much you are driving forward.

Try this. Start the car, turn the AC to recirculate the air, turn the AC on and go for a drive for 10 mins, pull over and wind down the window. Compare the outside air to the inside air, then you will see the difference.