You have inspected the water pump condition which seems okay and we know that it does circulate the coolent, probably not the culprit.

HG failure is not definately confirmed by water in the oil or oil in the water on these cars.

I have had the HG fail and been able to use the car daily for about a year.

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.with no steam and no oil in the water symptoms.

In my case the only thing you could not do was give it beans on the motorway.

You could use it every day on a and b roads without overheat, why, because it was all to do with the amount of exhaust gases placed into the coolant.

It was RPM and time dependant.

In my case

a tiny pin leak between the HG and the coolent passage was placing tiny amounts of gas into the coolant.

(hence no steam or oil contamination).

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.on a short journey it will not gass up the coolent sufficiently to displace alot of coolent back into the overflow reservoir and not lead to an overheat.

At motorway revs it would displace the coolent and guarantee a overheat in about 20 minutes.

I would definately sniff test to eliminate HG failure, why? Because it is essential to eliminate it from the list of problems FIRST as you cannot solve a bad HG by the replacement of other parts of the system such as the radiator, waterpump

, neither is it solved by refilling the system, bleeding, burping, flushing or going to your local toyota dealer xxxx.

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etc etc, your engine also has a history of HG failure.

If not the HG then you can proceed to query other system parts replace/check bits and pieces such as water pump, thermostat, radiator cap, radiator etc etc and also have the joy of draining, flushing and refilling the sytem with the correct amount of coolant.

At the end of the day the cause is going to be

The HG or

a leak in the system/ insufficient coolent

the radiator cap not holding pressure or

a fault with another part

( thermostat, radiator, water pump)