Since the smoked chicken quarters will be cooking for a long time you want to make sure that you are able to monitor the temperature. You are looking for a temperature of between 250º-300º. Too much heat and the quarters can dry out; too little heat and you will never hit your target internal chicken temperature of 165º. Most grills have the option of a display that shows the temperature but if your grill does not have one of these then you can always pick one up, they are usually pretty inexpensive.