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Okay if you find you are using up a lot of coolant then you need to put the cooling system under pressure like pump it up to 15 psi
and check the hoses ,water pump ,radiator etc and see if there is a leak .if no leak the pressure should stay 15psi for over 10 minutes .
If you see no external leaks but the pressure is dropping then you have a cylinder head gasket leak..this could be your problem as you said the engine at cold start up shudders ,you may find the coolant is leaking into one or more cylinders after you switch off the engine. common issue .
If you have every overheated the engine in the past then yes this could be your problem .
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