Because the truffles are made with fresh cream and no preservatives, they are perishable. They are best stored in a cool, dry place and eaten within one week (usually not a problem!). But if it looks like that's not gonna happen, put them in the fridge. More details:
Generally, they taste best when eaten at room temperature (around 68-70˚F) and when fresh. You can store them longer (a month +) in the refrigerator or freezer, but they may dry out a bit and won't taste quite as wonderful. If you go this route, be sure to place the truffles in an air-tight container or freezer bag. For best results, allow them to come to room temperature before opening (about an hour, or longer if frozen); this helps to prevent condensation from forming on the chocolate, which can change it's texture and appearance (but won't hurt you). Once back at room temperature, eat them promptly (within a day-ish).
I've heard rumors of people exhibiting extraordinary self-control and discipline, putting the whole box in the fridge & taking out just one truffle a day! Bah, humbug, I say.