Set the box of puff pastry in the refrigerator and let thaw for 4 hours or overnight. If you want to thaw one sheet, take that out of the box wrap it in plastic wrap, and thaw. 2. Take the puff pastry sheets out of the box and thaw at room temperature for an hour. 3. To thaw puff pastry quickly, wrap the puff pastry sheet in a paper towel and set it on a plate. Microwave the pastry for 15 seconds on high, then flip it over and microwave it for another 15 seconds.