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If the coolant system is full and the temperature gage goes up really fast ,matter of 4/5 minutes ,the problem is going to be the water pump ,the pump propeller is made out of plastic and with the years/heat ,it broke off the shaft and is not making the coolant flow through the engine.
Do you get good heat inside the vehicle with engine at idle ?
Remove the heater hoses from fire wall and start the engine to see if there is good flow ?
Let me know.