Does anybody know what the normal running temperature of an Arduino is if the ambient temperature is 20C?
No nobody knows that because you supply insufficient information. Not only do you need to know the input voltage the current being sourced by the Arduino to other devices, but you also need to know the thermal coupling between your Arduino and the environment, normally measured in degrees centigrade per watt. Finding that involves a lot of measurement.
If the Arduino had reached its peak temperature how long would it take to cool to the ambient of 20C?
Exactly the same information for the above question. These are things that are so specific to the particular setup that you are simply wasting your time asking.
Anyway what are you going to do with the answer, it has no relevance to your question.