Your problem sounds like a classic fan clutch problem.. Good that its a toyota and you can refill it with new silicone fluid.. (toyota sell this fluid as a replacement part)
check the fan for roaring when starting the engine dead cold, it should roar as the fan clutch is engaged, and once it gets to temperature it should start to couple and move a lot of air (and roar too) fully in sync with engine speed.
The bimetal spring in the centre should be clean and free of dirt and the radiator fins should be clean as the clutch's bimetal spring needs to get hot and warp out of shape to engage.
You will usually find the clutch has lost its fluid and is not coupling hard enough or at all for effecient cooling of the engine.
I just recently redid my mercedes fan clutch here in the US - but in my case I cannot fully open up the clutch like yours - and had to live with baking it in the oven and injecting silicone oil by guessing..