2001 Alero overheating problems

Hi. I have had my 2001 Alero since it was brand new off the lot. It has been a strong running car. It has had done work on it, most recently the mechanic I'm using has replaced the intake gasket, thermostat, hoses, and coolant reservoir because of the coolant leaking. After all that still having problems with the coolant leaking (but apparently not mixing in to the oil)....I've just been putting water in and I have to stop after driving about 10 minutes to refill the reservoir. The mechanic was going to replace the cooling fans because he said they weren't working but then he hooked up a sensor machine and there were no issues, so he ended up replacing the radiator because he thought there might be a blockage causing the water to boil back up into the reservoir, and the car overheating. The car drives great, but after about 10 minutes there is a type of sputtering. The mechanic is saying that he has replaced everything that can be replaced in the cooling system and that he thinks the head gaskets are bad. Anyone have this problem? At this point I'm not going to invest anymore to have head gaskets or a new/used motor put in. But if anyone has any ideas as to what else might be wrong I'd love to hear it. I just would like this car to either last a bit longer, or be fixed enough to sell.

are you getting any steam out the exhaust pipe? can also put a piece of cardboard under it and let it idle and see if you get any drips

When the car is cold check to see if the upper radiator hose is still pressurized. If your's is like mine you've got a head gasket that is blown from the #2 cylinder to the coolant passage to the left side of the cylinder. I didn't have any of the classic blown head gasket symptoms like milky oil, what I had was coolant disappearing with no visible leak and at first I assumed that I was losing it from the lower intake. According to the machinist that planed my heads he's seen quite a few of these where the owner claimed the car was never overheated and the leak developed around 130k. He believed that it was due to the torque to yield bolts going bad.

Allow the car to get hot, and shut it down......when it has cooled enough, attach a coolant pressure tester for the night....

Next day, remove plugs, and disable spark(remove power harness to ICM, 2 wire connector on passenger side), and disconnect harness to injectors....now have someone crank the vehicle(it won't start)......I can almost guarantee you will see coolant come out of #1 cylinder(this cylinder is on the backside of engine, first cylinder on the passenger side).....

Many times, an overheated car is diagnosed as a lower intake problem on 3.4's....but if you don't do a simple check on the heads, you will end up doing the same job all over again to get to the heads.....usually poor diagnosis.....