I am cooking a very large wedding cake (35 cm or 14 inch) and can't get the cooking time right. Is there a specific temperature I should use?
It's very difficult to cook a cake that large without a heating core.
Basically, it's a metal cup that you put in the middle of your cake so that you can get some heat conduction in the middle of the cake, like you would with a bundt pan or other ring-shaped pan. Unlike the ring pan, as it's a cup, you also fill it with batter so you have a plug to fill the hole that's created.
(and you generally need to fill the cup with either batter or something else heavy so that it doesn't float in the batter).
You also want to go with a lower temperature and bake it for longer -- this is not only because of the size of the cake, but you also want it to be more dense; if you're going to be stacking on top of it, you do not want it spongy, and you need to reduce the amount of open spring from a high temperature. I'd highly recommend looking for recipes specifically intended for large stacked cakes.
As medeira cakes tend to be slow cooking to start with, you might be looking at 1.5 to 2hrs to get it fully baked through.
Rose Levey Berenbaum recommends in The Cake Bible a baking time of 40-50 minutes for a 1 3/4" (4.5 cm) deep 14" (35 cm) layer, based on a standard butter cake formula.
The general principal is that the larger the layer, the longer the baking time at a lower temperature. I would caution you that like all baking times, these estimates cannot be exact, and you should rely on the appropriate doneness test for your particular recipe, such as the toothpick test.
I reviewed the Cake Bible by Rose Levy Beranbaum which to me is probably still the most authoritative source on cake baking, despite originally being published in 1988. Beranbaum does not specifically mention times for 14 inch cakes in her detailed recipes (her wedding cake recipes are for 6, 9, and 12 inch tiers which she indicates will serve 150 people), so the information above comes from the chart for recipe scaling (page 490).
She does indicate that the diameter of the cake pan does matter for the recipe, specifically that the larger the cake, the less baking powder is required proportionately. That is, each tier would then receive a specific amount of leavening depending on its size.
Beranbaum does not mention cake cups, but instead recommends cake strips or magic strips, which help promote baking even layers.
She also provides formulas for scaling various types of base cake recipes to various sizes, including the baking powder scaling.
Modifying cake recipes for large sizes is fairly detailed; I recommend consulting recipes or formulas specifically for this purpose. The Cake Bible remains a fantastic source, but does not have a recipe for the particular Madeira cake you have mentioned.