It depends greatly on how you intend to operate your vehicle. In racing, such an engine would demand a heat exchanger in the oil system. On the other hand, a street driven car might not...12qts is a lot for a street car to bring to operating temp just about anywhere, even here in Socal! True, you can use an oil cooler with a thermostat in the system for street, but I have always shied away from the added complication.
On many import sport cars, heavy duty trucks, etc. an oil cooler is std. The only street car I have installed an oil cooler on was my 290hp (at the wheels) T Coupe and, even that was a smallish piece. I use a 19 row Mocal on my ~130hp Mini and ~185hp Lotus...both with 10+qt.capacity wet sump systems. I did crew (back in pre history) on a IMSA GT Pantera with a 26 row Mocal on a 500+hp, 24qt dry sump system. On a hot summer day, oil temps hover around 200f on all these applications.
My vote is you probably won't need a cooler and, even if you live in Phoenix, you might need only a small one.
Rod