May be useful to change the thermostat and pressure cap like @circus
mentioned. I'd definitely try a pressure cap before a thermostat though (see bottom of my post for more details on why).
Have you seen any signs of leaks anywhere? Are you using Toyota Long Life Coolant (LLC)? Use a flashlight at night, look for any red liquid below where you park or on the engine. Look for crystals built up on the engine or radiator too, which are signs of dried coolant, which also indicate leaks.
Did you try running the cabin heat this last time time when it overheated? Could be you have multiple issues, and if with more coolant in the system now, if you were getting cabin heat when it overheated, then it points to a bad thermostat. If you still don't have cabin heat when it overheats, that's pointing to a coolant circulation issue still over a thermostat issue.
OBD scanners are great. I recommend you set it up to display coolant data live, and log it too, if you can. On a normally working cooling system, you should see the coolant temp rise until the thermostat opens fully at which point the temp should level off. For example, here's data from my 2014 as I was monitoring temps to see how long it took for the engine to reach normal operating temp. On my 2014, this is about 185 °F. Watch the blue dots. Note the temp rises and eventually hits 185 °F where it levels off and stays as I continue driving.
Watching your coolant temps and how it behaves may help narrow down the issue. Logging the data so you can graph it later like I did would also be useful.
Electric coolant fans can turn on at any point, even when the vehicle is off (key off). Some vehicles, not sure about the 1st gen Sienna, will occasionally run the cooling fans after the engine is shut off for a few issues. I believe my 3rg gen says it may run the fans for a bit after the engine is turned off, depending on how the engine was used, ambient temps, and engine temp. I drove a 1991 Honda Accord when I was a teen, and on warm or hot days it would always
run the cooling fans for a couple minutes after the engine was turned off. I believe this was to prevent vapor lock on a hot engine restart. So many people said "your car is running"...nope, just the cooling fans doing what they do. In any case, on a vehicle with electric cooling fans, always keep fingers and loose clothes away from the fans unless the battery is disconnected, as the fans may engage automatically even if the engine is off.
That said, your fans not turning on when your engine was overheated may be an issue too. Is your drive mostly highway, or is it stop and go? On the highway, the fans should not need to turn on to prevent overheating, but if it's getting overheated they should definitely be turning on. I don't have the FSM (factory service manual) for the 1st gen, but the FSM for my 3rd gen says with the AC off, the cooling fans should turn on at low at 207 °F, and go to full speed at 216 °F. They should start slowing down as it cools to 212, and turn off when it cools down to 203. At this point, the temp gauge shouldn't even have budged off the "normal" location, so by the time the temp gauge starts going up, the fans should definitely
You can download sections of the FSM if you get a 2-day subscription to techinfo.toyota.com (what I do, printing sections to PDF for later use). This will tell you how to troubleshoot the fans and other parts of the cooling system, and what temps the fans should turn on and off at.
Failing that, if you turn the AC on, do the fans come on immediately? The fans should run anytime the AC compressor is running, regardless of coolant temp. If the engine isn't overheated, the fans should cycle on and off as the compressor cycles on and off. If they don't, that would point to a fan issue.
A Little Bit of Cooling Theory:
50/50 antifreeze has a boiling point of 223 °F. Coolant systems are generally pressurized to about 15 psig, which further increases the boiling point to 253 °F. A coolant pump, which is driven off the engine (either by the accessory belt or by the timing belt, depending on the engine), constantly circulates coolant through the engine and the passenger cabin heating core(s). A thermostat is used to allow coolant to come up to the normal engine operating temp of about 175-200 °F, depending on the engine design. There are bypass loops that allow the coolant to flow through the engine and back to the coolant pump inlet while the thermostat is closed.
Once the coolant is hot enough, a thermostat will start to open, allowing coolant to flow into the radiator, or from the radiator (depending on thermostat location), which brings hot coolant into the radiator and lets cool coolant flow into the engine. The thermostat is a simple mechanical device that uses wax melting and freezing to open and close the valve. This action is proportional, allowing the valve to be fully closed, partially open, or fully open depending on coolant temp. If everything is working correctly, it will maintain the coolant temp at the design temp.
Fans on the radiator are used for additional airflow. Originally, these were engine driven fans, generally with a clutch to engage or disengage them. Now, they are pretty much exclusively electrically driven. They run when the AC compressor is running, regardless of coolant temps, otherwise they only run when the coolant gets too hot, which is some point above where the thermostat is fully open. When driving on a highway, there is plenty of airflow from driving, so the fans aren't needed. They are only used if the vehicle is driving slow or stopped, as there is insufficient or no airflow to maintain coolant temps in these cases.
Coolant always circulates to the heater cores in the passenger cabin, regardless of coolant temp, unless the car regulates heat into the passenger cabin by a coolant flow valve instead of using the traditional air mix damper, which isn't common.
If a vehicle overheats, but full cabin heat is requested and it blows hot air, this indicates a thermostat and/or fan issue, as the coolant is circulating fine if you are getting cabin heat, but it's not being cooled sufficiently.
If a vehicle overheats, and full cabin heat is requested but it blows cold air, this points to a coolant circulation problem, because if coolant isn't circulating, you won't get heat to the heater cores, so no hot air will blow from the vents. Coolant circulation problems are generally due to air in the coolant system caused by low coolant, because air in water pumps makes them work poorly, or not at all. Since the coolant pump is driven off the engine (except some modern cars will use electronic cooling pumps), it can't be the pump itself has failed, unless it seized and a belt is slipping, but you'd definitely hear that and your belt wouldn't last long...
A failed pressure cap could cause these issues, as with no pressure the coolant may start boiling and creating steam pockets in the coolant, which could lead to circulation issues. So replacing the radiator cap wouldn't be a bad idea.
A coolant leak will definitely cause these issues, so the leak MUST be found and fixed!
It certainly won't hurt anything to change the thermostat, but I can't see that being the issue based on the information you've provided about your problem. If you decide to change it anyway, just for kicks I'd throw it into a pot of water and put it on the stove with a thermometer. If it starts opening around 180 °F, the thermostat was fine.
The vent mentioned by @circus
is a good point too. This vent (called a jiggler valve) allows air trapped in the system to help work it's way out of the system. This vent must be installed facing up when the thermostat is installed. Here's a picture of the thermostat I installed in my 2014, as I changed the thermostat when I changed my water pump, because I had to remove the thermostat anyway for that job. The jigger valve is correctly installed at the top of the thermostat. It won't do it's job if it's not at the top when the thermostat is installed.