"A new radiator didn't fix the problem"
I've stripped mine all the way down to the heads, and had the valves and heads remachined, installed new gaskets, etc. The head gaskets were in good shape, no leaking.
I had exactly the same problem as far as mystery overheating. Of the two main causes of overheating on the 2vz-fe 6cyl (including those which dem2527 and others were trying to get me into) were, gasses in the radiator, failure of the fans:
Air/hot gasses in the coolant system, usually after a chronic overheating caused by fan failure (correctable). This system requires a Lisle or Worthco radiator funnel kit. The funnel kit has a large capacity (around a gallon of coolant), and fits tightly with the top of your radiator. It allows you to keep the radiator fluid above the uppermost level in the engine, allowing hot air to escape, steam, and coolant to go in. The longer way around, is to fill the system:
** Fill it. Don't cap it.
** Start the engine
** When the engine has started to warm up a bit, Open the bleed bolt. It's in the back, follow the top radiator hose back to the engine, this is the hot return. There is a bolt right next to the hose connection. Open it up and you will see a little hole near the top of the threads, the bolt is hollow and those let hot coolant gasses escape.
** Keep the radiator topped up, and as the engine runs hotter and gasses escape, eventually the foamy fluid will appear, then just fluid. Close the bolt, check the level, close the radiator cap. If you had the lisle funnel kit, you would stop here.
** Overfill your reservoir.
** Drive the car a little bit, until fully hot.
** It's at this point that it's a good idea to stop and check under the hood. When your needle is getting about half-way on temp, you should see the fans operating under the hood on the radiator. If you DON'T, this is a known failure of the 2vzfe. I spoke with a woman who spent 2,000 on the suspension on her identical car, and then the engine blew up because the fans failed around 200k, just like they stopped on mine, precipitating the overheating problem secondary to fan failure. Someone familiar with correctly functioning 2vzfe fans can comment on whether they work at all at lower temps. I never had them working on mine, and there are five pages of schematics to trouble-shoot the circuit.
** IF or IF NOT the fans are operating, shut the car down in either case.
** IF the fans are NOT operating, pull A/C relay #2. The round, metal relay underneath the hood near the battery in the box with some other relays. This turns off the passenger side fan. Open and remove the glove box, and remove A14. You will see two boxes, the top one upside down with the wiring hardness connector oriented up, the other one underneath, pointed down. I think A14 is the one on the bottom. This will cause (I think it's the brown wire) to be OPEN, causing the drivers side fan to run on full. If you want to stop this fan, ground the wire. Yes, your A/C may not work for the moment, but the driver side fan will run at full speed pulling about 15 amps, and the car shouldn't overheat. I will eventually replace 5 pages of overly complex nonsense with a PVM box that directly monitors coolant temp and runs the fans at whatever speed necessary. ($150).
** Let it cool for 20-30 minutes depending on ambient temp. Keep an eye on the reservoir level, and when it starts to drop, the car's cooling system is sucking in coolant to replace the gaps. Basically, you run the engine, heat it up, let it cool and keep the reservoir topped off, and do this a few times and the car will force out all gas and fill itself.
I replaced the stock radiator with an OSC model 21 radiator. Haven't looked back since. It cools better than the stock radiator, and seems built better.
1991 Lexus ES 250 (A rebranded 91 DX Camry v6)
Castrol Syn 0-40w, or Mobil1's 0-40w
Fram Ultra Syn filter X8A (same as Landcruiser, 3x capacity)
ATF&PS Chevron MD-3, 5gal/$61