It could either be the water pump.
If the fluid is not circulating throughout the system, this would result in the car overheating. This could be due to either the water pump, radiator, or both.
I would recommend a "backflush" of your fluids. If there is some sort of blockage or corrosion, a backflush may help you that could be a problem too.
I'm not too familiar with the TD engine, but I would think that the cooling system should be similar to a non-diesel model.
To backflush the system, you would have to first drain the fluid, then flush water via the heater hose going towards the engine block. As you have the water flowing, turn on the car and turn the heater on to HIGH.
This allows the water to flow through the whole system in reverse, eventually out from the radiator.
If you see a lot of corrosion coming out, then you may have to change the radiator as well.
Of course, make sure you do this when the engine is cold.
I hope this helps you out.
Good luck with the car...
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Regards,
Toyrolla
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88 I4 Slushie *sold*, 89 I4 5Sp *sold*, 89 V6 5Sp *sold*, 82 Corolla, 72 Datsun 510, 88 Toyota Minitruck.