When my car warms up the heater blows out warm but gradually gets cooler and cooler after about 10 min. It will stay cold ( about three degrees above outside temp.) It does this on cold days. And after you start it later that day, it will still blow cold air. On warm days it will not blow warm air at all. It's always cool air.

It may be the valve that controls the amount of water entering heating core but I'm wondering if your engine thermostat isn't stuck open. This is what controls the coolant temperature in your engine. It closes off while engine is off. It will remain closed after you start your car until the water warms to a certain temperature then it starts to open enough to keep your car at the proper operating temperature. If it stick open then it will take a lot longer for the engine to heat up and on smaller cars might never heat up enough for your heater. If you live in very cold climates such as where I live in Wyoming, we have to change to a higher degree thermostat so we have a good heater when it's 30 below zero.

Be very cautious here but one way you can check this is to put a piece of cardboard in front of your radiator and stop the airflow that cools your engine coolant. THIS WILL CAUSE YOUR CAR TO HEAT UP AND CAN CAUSE ENGINE DAMAGE IF IT OVERHEATS. Don't completely cover the radiator but if your heater warms up when you put the cardboard in front of radiator it's a good sign that your thermostat is stuck open and needs to be replaced.