Heater system has distinct noise like a tapping. If the temp is in a cold setting then the noise goes away. The warmer you turn it the noise comes back at a certain level , then gets louder.

SOURCE: 2004 Chevy Silverado Heater blows cool air

Check blend door actuator for operation

SOURCE: vw t4 '03 tapping noise

Hi,

Next time it's tapping at idle, press the brake pedal hard several times. If it stops tapping then gradually returns then it is a noisy vacuum pump.

It can go on like that or years (if you can put up with the tapping that is!) if you start to loose servo assistance while manovering then it's time to change the pump.

Hope that helps.

SOURCE: clicking noise behind ac /heater control on dash

the problem is with the blend door it controls the blend of hot and cold air. there is a small electrical motor that can go bad or they can hang up
you will probally have to take some covers off to find out whats going on

SOURCE: ticking noise

you need to give us more info about your car, based on your info i would say one of your valve lifters is bleeding off pressure when the engine is off, you can try putting 1/2 qt. of automatic transmission fluid in your engine oil, atf is a good cleaning agent and may clean your lifters up. i have done it many times

SOURCE: Ticking/Tapping when car starts but goes away???

I had what sounds like the exact same problem. It was an exhaust leak from the left (driver's) side exhaust manifold. This engine has a history of the manifold bolts breaking and causing the exhaust leak. The engine is also used on some Dodge vehicles. It sounds like a tick and I almost mistook it for a bad lifter. I took it to the local Jeep dealer who confirmed the exhaust leak. I replaced the left manifold completely and replaced bolts/gaskets on both sides (left/right) and it fixed the problem. Be careful, as the dealer tried to gouge me on the price. You are looking in the ball park of $600 parts/labor. I got parts for $120 and it took the better part of a work day to do the job.