RPM fluctuation when the engine warms up

When does this occur? When idling in "park"? While driving at highway speed?

The first thing is to look for vacuum leaks. Pinch off various vacuum hoses while the engine is running and the problem is occurring. If you pinch the hose leading to a leak, the idle speed should go down and stabilize. You can also pour water over the top of the engine while it's still cold to see if it gets sucked in anywhere. As a last resort, your mechanic can use a smoke machine to inject a white, non-toxic smoke into the intake manifold, then watch to see if it sneaks out somewhere.

The next step is to use a scanner to view live data to see what the Engine Computer is seeing and responding to. It will show the desired engine speed and the actual engine speed. If the desired speed is fluctuating a lot, that is in response to a sensor reading or operating condition. Those will show up in the list of sensor data. If the desired speed is holding steady but actual speed is not, it's almost always a mechanical problem such as that vacuum leak that the computer doesn't monitor that is causing the unstable speed.

If the knock sensor is detecting what it thinks is spark knock, the Engine Computer will retard ignition timing in an attempt to stop it. Varying timing will cause idle speed to vary. I think I'd try a higher octane fuel first to see if that helps.

Loose and sloppy timing chains can slap against the cover and be detected by the knock sensor too. Your engine does use a chain, and not a timing belt, but the mileage you listed is much too low for this to be a valid suspect.

Normally I would say there is wear in the bushings the throttle blade rotates on and the throttle body needs to be rebuilt, but there's two problems with that. First, this shows up due to very high mileage, as in over 300,000 miles. Yours does not have that much wear yet. The second problem is your car most likely uses the "throttle-by-wire" system that put Toyota in the news a few years ago. I've never autopsied one of those assemblies to see what's in them, but I do know they use a really strong motor to turn the throttle blade. I would start by looking for something that could have occurred on the assembly line, like a mis-positioned gasket, a cracked housing, loose mounting bolts, and things like that.

I know this can be hard to tell, but if it looks like there's something that could be a common or recurring problem on many cars, there may be a recall or service bulletin. Dealers will take care of recalls at no charge to you. Those are issued for safety and emissions concerns, and some manufacturers issue them for customer satisfaction concerns.

Service bulletins are issued to help mechanics find the causes of elusive, but common problems. They are only meant to save time. You have to pay for the repairs if the car is out-of-warranty. The bulletin will specify part numbers and repair procedures. I would leave anything related to throttle-by-wire systems to the dealer. Most independent mechanics don't want to work on them because anyone who touches it could become party to any future lawsuit, and it's only a matter of time before another malfunctioning computer sends a driver on a wild ride. That will probably change in the future when the independent shops learn more about these systems. There have been many instances where mechanics were baffled by something new, like Chrysler's "alternator", "Lean Burn" Engine Computer, anti-lock brakes, and air bags, and GM's "HEI" ignition systems, so they refused to work on them. Now those are very common and simple systems. This is the first one though where making a mistake can kill someone, hence the reluctance to work on them. This is also why I don't recommend you work on it unless you see something obvious and simple.

I'd be pursuing the throttle body. It's apparent that water blocked something and stabilized the idle speed. There may be a vacuum hose or port in there, or something else that is allowing vacuum to leak.

No. The Engine Computer doesn't know or care about tire side, but if you changed the outer circumference, you changed an alignment angle called "scrub radius" that is important for proper handling and braking. Lawyers and insurance investigators know all about scrub radius and will use it against you if you're involved in a crash caused by their client. They will say you were partly at fault because you were less able to avoid the crash, and they will be right.

Besides the legal ramifications, you also need to have the new tire size programmed into the Engine or Transmission Computer so the speedometer will read the correct speed, and if the vehicle has anti-lock brakes, all four tires must have the same circumference.

Dandy. I'll reserve my thumbs-up for a few days to be sure the problem is solved, but I have high hopes.