Lexus GS 300 Code P0505, Can't find problem

Hello, I currently own a 2006 Lexus GS 300 with 140k miles that I bought a few months ago.

My car was running fine until one day the red battery light came on. I took the car to NTB and they replaced the battery, even though it was probably the alternator and they knew it. It didn’t fix the problem. A couple hours later when the car was not running, there was smoke coming from the alternator. I took it back to NTB and the alternator was burning red hot. They spent an hour spraying it with water to get it to cool down. Then they replaced the alternator and all seemed well, until later the same day I got check engine light code P0505, which is an idle control system related problem. After many drive cycles (about 2 weeks driving to work every day, about 400 miles) the light stayed on, and I began to notice the car would dip significantly in RPMs when idling, down to 300 at times, and the car would shake as if it was a big truck. It would fluctuate in RPMs between 300-700 or so when idling. It didn’t do it every time when stopped but a lot of the times it did. NTB couldn’t figure out what was wrong and they stand by their work. I took it to the Lexus dealer, thinking they probably know best. They checked for all the common stuff (vacuum leaks, throttle body buildup, IAC, and a few other things). They cleaned the throttle body but couldn’t find any other problems. They cleared the code and drove it and the check engine light didn’t return. That is, until I got the car back. It came back on the same night when I was driving it myself to see how it idles. From what I could tell, it seems like as I come to a stop, the car would stick to a certain RPM at each stop rather than fluctuating. For example, I’d come to a stop and it would sit at 600rpm. Come to another stop and it would sit at 800. Another and it would be 500. Seemingly random but it didn’t fluctuate like before, still shook though when it decided to stick to lower RPMs. Waited a week to see if it actually was learning this time, didn’t go away. Took it back to NTB and they double checked and confirmed there was nothing wrong with it as far as they could tell. Now, it seems to have reverted back to the original rough idle where it would fluctuate a lot instead of just sitting at a certain rpm (whether that be low or not).

Some observations of mine:
-If car is idling in park and it dips down to 400, turning off AC will make it go back to 900 or so and sit there for a while. Turning back on AC will dip it back down to 400. Eventually it will dip back down to 400 even with the AC off.
-Battery light comes on at redline, and then turns off as soon as shifting (didn’t do this before)
-Fuel economy is horrendous. Used to average 24, now am getting about 18.
-Power seems to be slightly less. I don’t measure my acceleration times or anything so I can’t confirm this, but it feels like it.
-Engine temparture will drop a bit when idling at low-ish rpm for long enough. Not a lot but enough for me to notice the gauge is lower than it should be.

I also talked to a mechanic friend who knows a lot about Toyotas and he is unsure of this issue. Nobody seems to have ever had this kind of problem before, especially on a Lexus with relatively low miles. Lexus dealer mechanics have never seen this nor has NTB manager and technicians. Could this be related to the cold (It’s around freezing where I live, Chicagoland area). Could the burning alternator have damaged something nearby to it, and if so, what could it be? Why can nobody find the problem? Could the alternator have broken the ECU or some other electrical component?

I would greatly appreciate if someone could give me any possibilities. I’m stumped and don’t know where else to go at this point, nobody could identify the problem. I just want this to get fixed.

Inspect the air intake tube from the air cleaner to the throttle body for cracks, they become rock hard on that vehicle and crack near the throttle body when trying to remove them. Air leaks in the intake tube can cause an unstable idle.

Is this something that I can do without being much of a mechanic? I have not had much experience repairing cars. Also, wouldn’t someone have checked and noticed this, considering that Lexus did a thorough examination of it and found nothing? I will see if I can check it myself though.
@Nevada_545

Checking air intake hose for leaks as Nevada suggested. I’d also be looking for melted wires or any heat damage and or water incursion problems to stuff near the alternator.

So you stress the engine like this a lot? Not good for longevity…

I’ll look at the wires too, thanks.

And no, I don’t do that very often. I usually drive normally.

If no leaks are found in the intake tube, unplug the connector from the alternator and go for a short drive, if the engine idle stabilizes the alternator may be the problem. I have seen odd side affects from cheap replacement alternators with excessive AC ripple and voltage spikes.

If I look at the title of your post, it says Error Code P0505. That is an Idle Air Control (IAC) valve problem. Likely a failure based on your description. I don’t know who gave you that code but if NTB did, stop using them, this is clearly an IAC issue. Replace the IAC valve and cleaning out the passage is the most likely repair. Doesn’t matter if NTB “stands behind” their work if they are incompetent.

Next, the alternator repair. I think the alternator belt is slipping since at high RPM the red warning light appears. It may be a glazed pulley, it may be a failed tensioner, it may be a damaged belt if that wasn’t changed after the alternator roasted itself. Again, avoid NTB.

I’d be a bit concerned about the Lexus dealer, too BUT, if the check engine light was not on, they didn’t have much to go on.