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Yes, some modern rads are shite. Check for fakes and unbranded never heard of rads. An example is getting motorbike, honda NC30 water and oil rads from china. Very hit and miss while car parts are being copied and are poor quality. There are lots of ways that rad makers are trying to prove that their products are genuine.
The cold internal heater rad does not inspire confidence too. Is it an air lock and is that air lock caused by a blocked rad? When you take the thermostat out back flush the system in the opposite direction to the normal water flow. Maybe disconnect the heater water pipes and back flush that to see if there is a blockage?
If the body is in good nick I'd try my best to keep it as decent MK2 golfs are only going to go up in value.
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If the thermostat does not open it will not circulate the hot water to the radiator to circulate it for cooling, ergo the fan switch will not get hot water to it to cut the fan in.
A lot of modern engines will over heat with out the rad cap in as the pressure build up raises the boiling point of the coolant, without the pressure small pockets of coolant in the hottest part of the engine can boil up creating steam which then forces the coolant out.
I would replace the thermostat first.
checking the radiator is quite easy remove the hoses and force water through it to see if it flows OK
It is looking like a blocked/clogged radiator to me.
Any decent rad places that could recore to a higher spec aluminium core, or would a modern rad be a decent aluminium core.
But lets see if the headgasket has failed again.