Hello, there I have a 1992 Es300 had the same exact problem replaced the most suspicious culprits that would be behind overheating (water pump, power steering hose, radiator, thermostat, even ran the little blue gels through the radiator system to find a leak nothing still over heating and coolant over boliing). One simple thing you oughta check is the controll fan unit located behind the glove compartment. This little gadget could be the root problem of your woes. The CFU has little diodes ( small battery looking thingy's) if you look carefully at the top of one of those diodes and it has a bulge it is blown. So you will have to replace the whole unit. It doesn't cost that much the only issue is the labor involved in getting to the control unit it is a pain. The CFU controls the Fan's speed mainly telling the fan when to kick in on high gear to cool the engine and prevent over heating. I worked long and hard on this believe me one simple thing.
Later on when taking a trip I blew a head gasket and instead of doing the heads I replaced the whole block with a used one that was checked for compression and all and was guranteed on the mileage. Replacing the block was much cheaper than getting the heads done since the engine was already knocking. I hope this helps.