Preheat oven to 325°F. Mix graham cracker crumbs, 1/3 cup sugar, and melted butter. Press into the bottom and up the sides of a 9-inch springform pan. Bake for 10 minutes then cool.

In a large bowl, beat cream cheese, 1 cup sugar, and lime zest until smooth. Add eggs one at a time, mixing just until blended. Mix in key lime juice, sour cream, and heavy cream until smooth.

Pour filling into the prepared crust. Bake in the preheated oven for 55 minutes or until the center is almost set. Turn off the oven and let the cheesecake sit inside for 1 hour with the door slightly open.

Chill in the refrigerator for at least 6 hours before serving.