OK – this is the deal, egg white starts to coagulate in the range 62-65 °C. At these temperatures it is the most heat sensitive protein, the ovotransferrin, which constitutes 12% of the egg white, which coagulates.
The major protein of egg white, ovalbumin, makes up 54% of the white and doesn’t coagulate until the temperature reaches 80 °C. The yolk begins to thicken around 65 °C and sets around 70 °C. In other words cook the egg to 70 °C and you should have perfect scrambled egg – not too runny and not too dry 😀