How is baking time and/or temperature adjusted when scaling up a cake recipe from a 9x13 pan to a full sheet pan?
For 9x13 cakes, typically the batter is thicker. So you want to cook a little longer at a lower temperature to make sure that the inside gets cooked without burning the outside.
For a sheet pan, typically cooking is done at a higher temperature for a shorter period of time. If you cook too long at the lower temp it runs the risk of drying out.
If you were using the same amount of batter and just making a thinner cake, like I do, I would recommend increasing the temperature of the over by 25 to 50F (depending on the recipe you use), and start checking after about 15 minutes in the oven.
However, if the sheet pan batter ends up with the same thickness as the 9x13, don't change the temp or cooking time.
Time is tricky - since there can be hot/cold spots, I would cook 5-7 minutes, rotate the pan 180 degree, then cook another 5-7 and start checking. Make sure the cake springs back, and isn't doughy in the middle (no wiggling).
Best resource I have for cakes: Baking, by James Peterson