As mentioned, replace your thermostat and radiator cap. Since buying my 85P new, every few years it starts to intermittently overheat some. EVERY time, it's been the radiator cap. These seemingly simple devices perform multiple functions and cooling system pressure testers only test one of them. They're great for determining if your cooling system can hold pressure, but simply aren't able to fully test caps. Radiator caps are cheap and simply don't last very long.
Here's what happens. After a hot shutdown, the coolant expands some and is pushed past the radiator cap into the overflow tank. When the engine cools down, the coolant contracts creating a vacuum which, if everything is working correctly, sucks coolant from the overflow tank back into the engine. For this to work, not only must the radiator cap work correctly, but there must be a good seal from the radiator to the overflow tank. Make sure that the hose from the radiator to the overflow tank is good and that the rubber seal in its cap is there. Also, if there's any coolant leaks, a good vacuum won't be created and less coolant than needed, or more likely none will be drawn back into the engine when it cools. A pressure tester will confirm if your system can hold pressure and will therefore also be able to create a vacuum to suck coolant back from the overflow tank.
When the radiator cap fails, on shutdown some coolant will still be forced into the overflow tank. But when the engine cools, it won't be sucked back into the engine. Then the engine will overheat sooner and more. I'm sure you can see that it doesn't take long before this becomes a much bigger problem.
Another potential problem area is the screw type hose clamps. They're known to loosen up over time. Yes, you can use Loctite on them. But I finally removed all of them and replaced them with the original spring clamp style ones. They don't loosen over time.
Thanks to ddd228, I've also added a simple cooling system bleeder to the top rear heater hose, the one from the center rear of the engine to the heater control valve. It's the highest point in the cooling system and bleeding all the air out of the cooling system after a coolant change or whatever is MUCH easier and faster than raising the front of the car, etc. Dave used a cheap garden hose repair kit to do this. These come with a male and female barbed hose fitting and clamps and are typically used to repair a hose with a cut or tear.
So after having this issue a few times, I started using a Sharpie to write "Check Me First" on my radiator caps. No matter what Sharpie claims, it's NOT permanent, not even close. The last time this happened, it had been quite a few years. I checked everything and when I'd ruled out everything except the radiator cap, upon close inspection, I could faintly see a couple of letters of my Sharpie note to myself. DUH! So on its replacement, I used some black touch up paint and painted "Check Me First!" on it. Hopefully, this will help should brain fade happen again, and it surely will!
If your car only overheats in stop and go traffic or when idling for a while, your fan clutch has probably failed. They can usually be brought back to proper operation by replacing the fluid in it. It seems that over many years, some of the fluid can leak out and once enough does, it'll fail to couple when it gets hot. There's articles on the net about how to properly do this. One important note is that you don't have to use Toyota specific fluid for this although it's still available. The silicone differential fluid for RC cars is exactly the same, much cheaper and easily available. The proper viscosity is 3000 cSt. It's available in 2 ounce (59ml) bottles which should be enough to completely replace the fluid although this should be verified.
Why bother doing this vs just picking up a new one? It's much cheaper and of 3 replacement units I've had experience with, they all either had problems out of the box or quickly failed.
Another possible issue is with the nylon fan itself. Over time, these tend to soften and individual blades will start to warp from heat. With the engine running, it'll appear like the fan is wobbling. But looking closer, the water pump bearing and fan clutch are just fine. Eventually, one of the blades will bend forward enough to catch under the top rear edge of the top radiator tank and / or the fan shroud. The fan is NOT sucking the shroud backwards although it can appear that it did. This can happen even without the shroud in place. The fan bends forward trying to pull air through the radiator and the hotter everything is and the higher the RPM, the more likely this is. The solution is to replace the fan.
FYI, there's a lot of reasons why nylon fans are a good thing vs metal ones. Should you ever get a hand in one, you'll likely end up with a bruise or two and maybe a cut at worst. But you'll still have all of your fingers! And I've never heard of nylon fans losing blades either. Hope this helps.