Pumpkin pie, cheescake, and key-lime pies are all examples of custard pies. With all of them, you start with a hot oven, typically 425' F. After ten minutes, the heat is turned down to 325 and the custard then bakes an additional 45 minutes, or longer. If the pie isn't cooked long enough, the filling won't get hot enough to set.
It is heat, and the proper ratio of egg to liquid that causes it to set. For instance, with my cheesecake recipe, if I use the above listed timing, the filling still jiggles a bit when the pie is tested. I know it's done, and that it will bake longer as it cools in the oven with the door open. It is velvety-smooth and creamy. If I cook it 15 minutes longer, before testing, it is much more firm, and a bit on the dry side, but still very good. If I cook it ten minutes less, it is soup.
Most custard pies that I know of use 3 large eggs, and about 12 oz. of liquid, plus sugar and flavorings.
Just some examples.
Seeeeeeya; Chief Longwind of the North