Most parchment is rated for up to 450°F, so if you are baking this in a 425° oven you should be just fine. Just make sure your rack isn't too close to the heating element. For the grill, either use gas or make sure you don't have large flames. Cooking off to the side of flames for an indirect heat is also a great idea. Your paper should brown but not burn. If you are truly worried, you can always use heavy duty aluminum foil instead of parchment.