I've had them in the cooler for almost three hours. I know others here have gone longer. It depends on the internal temp when you put it in, how well wrapped it is and how good the cooler is. I take mine to IT of 200 or so, wrap immediately and place in a large Playmate cooler. It's the perfect size for the ones I do and it's completely stuffed with the butt and towels.
If you have it in the cooler now just insert your probe thermo-meter into it and don't let the temp go below 140° ish. That the temp where bacteria can start to grow. But I have left one in a cooler for almost 6 hours.