It depends how "quickly" is defined. I haven't timed my car but I'd judge that your quoted one to one and a half minutes isn't too wide of the mark. The official temperature for the fan to stop running is 96 degrees not 95.
Remember also Pete that your cooling system is not perfectly sealed. This will cause temperature instability. When you carry out the necessary repairs you will notice an improvement.
Simon
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"Whatever is rightly done, however humble, is noble."
Sir Henry Royce.
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