1 Place the pork shoulder fat side up on the top rack, cover with the lid, and bring the temperature up to a constant 225°F to 250°F, using the vents to regulate the temperature.2  If your grill doesn’t have a temperature gauge, you’ll need to purchase a digital barbecue thermometer. After the pork shoulder comes off the grill, let it rest for at least 15 minutes to allow the juices to settle back into the meat. 2  Remove any large chunks of cooked fat. 3  There are several ways of serving pork shoulder. 4  The most common way is to “pull” it apart, using two forks to pull and separate the strands of meat.