Why does hot food placed in a picnic cooler keep cooking?
What you call a "modern picnic cool box", I assume, is also known as a "cooler" in other parts of the world.  This is generally a well-insulated, most often plastic, container.  It could be hard-sided or made of soft material.  The container and insulation is designed to maintain a consistent temperature.  So, cold things remain colder longer, but also hot things remain hotter longer.  It's the same principle at play in an insulated drink container (Thermos is a common brand).  Also at play in your question is a phenomenon called "carry over cooking".  Food retains heat and continues to cook, even after it is removed from the heat. Usually not a concern with a stew, which slowly cools when you are finished cooking.  However, when you place your stew into a cooler, fairly soon after it is removed from the heat, it will take much longer to cool.  Carry over cooking will be impacting your final product.