Doubling a red velvet cake recipe
If you're making the same thickness of cake, and it's a relatively thin cake (suggested by the fact that you're using a sheet pan), you typically do not need to change the time and temperature.  So if you've doubled the recipe and doubled the area of the pan, you don't need to make any changes.

A larger area cake will rise more as there won't be as much edge that will set before the rest has risen.

If it's a thicker cake (the batter is more than 1/2" / 1.25 cm deep before baking), you'll want to turn down the temperature and bake for a longer time.  If the batter is an inch or more deep, you may want to consider cooling strips and/or a heating core.