You can, but I cannot think of a single good reason why you would.
325 F and 350 F are not that far apart; they may even be within the accuracy of most ovens, especially older ones.
When you bake the cake, the two main modalities of heat transfer (radiation and conduction from the air in contact with the surface of the cake) begin to heat up the surface of the cake at the cake/air or cake/pan interface.
Within the body of the batter, conduction begins to transfer heat into the center of the cake.
At the same time, on the top surface especially, water can evaporate, faster than it is replenished from water diffusing from the interior of the batter. This allows crust formation to begin, with drying of the surface, and heating of it to levels above 250 F or so which allow caramelization and Maillard reactions to begin in the crust.
The interior of the cake can never exceed the boiling point of water, and so browning does not happen.
Thus, the higher the temperature, the greater the difference between the surface temperature of the cake as baking proceeds, and the interior of the cake. This has several consequences:
- Thicker cakes should be baked at a lower temperature to permit them to cook through before the surface is over-baked; similarly, thinner cakes can be cooked at a higher temperature
- The higher the temperature, the more rapidly crust formation proceeds, and the more slowly the center of the cake bakes
However, 25 F is not enough of a difference to worry about in most cases.
Starting at only a slightly higher temperature, when the water from the surface is not yet evaporated, will have only a minimal effect on any of this. There is little, if any point to doing so.
Experimentation is the key in any recipe development, informed by the effect of the variable under investigation.
In baking cookies, the affect of the oven temperature will effect:
Spread. Cooler temperatures will allow the cookie to take longer to set, and so it will have longer to spread before it sets.
Height. This is the compliment to spread; cooler temperatures will allow the cookie to spread more, so it will have less height.
Drying. Cooler temperatures will allow the cookie longer to express steam, providing a somewhat dryer cookie. At its extreme, you can make quite dry, wafer type cookies.
Evenness of cooking. Cooler temperatures cook allow the to cook more eveningly from the outside to the inside. Hotter temperatures may allow, for example, browning at the edge or surface while the interior is under-cooked.
In most cookie recipes, the difference between 350 and 375 F may actually be smaller than other uncontrolled variables like the type of oven, individual oven variance, type of cookie sheet, size of individual cookies, and so. Additionally, within certain limits, there is a trade off between time and temperature.
For these reasons, you will need a high degree of consistency if you are doing dry runs to try to determine the optimal temperature.
Best Answer
I have found that as long as the two recipes don't have a huge variation in baking temperature (and as far as I have found, 25 degrees is not that huge of a variation), as long as they bake for a similar amount of time, it turns out okay. What I usually do is set the oven at the lower temperature for the indicated bake time (in your case, 2o minutes), and then check them at that time to see if they are baked. Usually they are, or they are really close and only need 2-5 minutes more to be done perfectly.