I have the same problem on my 02 Grand Am 3.4L 'Gurgling sound coming from behind dash'
I had suspected a head gasket leak or air in the cooling system since the water pump was changed out two months ago, but I have checked the following; the coolant level is normal, the oil dipstick level and texture and color is normal, the engine temperature stays around 200 degrees, the heater puts out plenty of hot air, the car doesn't smoke when initially starting the car in the mornings, the engine runs smooth, and no collapsed coolant hoses.
Every thing you have mentioned is all normal except the gurgling noise. The only thing I can think of is there is still a little bit of air in the cooling system. Make sure the reservoir is at the appropriate level, and just keep checking the bleeder to see if you can get some air out of the system.
I agree with Rowefast and had the same issue on a 05. If you warm the car up and put it on defrost high heat does it blow HOT air or does it fade after a while? If not the heater core is most likely air locked, happens often and the bleeder screw doesn't help. The faster the heat fades the more air you have trapped. You need to break the hose apart from the heater core to the pump and rev up the engine to get the air out. I cannot remember if it's the top line or the bottom but if you follow it under the throttle body it runs to the water pump. The quickest and least messy way to do it is to pop the line apart then put it half on, get a helper to start the car and take it up to 3000 rpm, quickly pop the line apart and reconnect when the fluid comes, you may need to block the tube going to the water pump but if you fast enough this works. Then just top up the system and you are good.
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