You'll definitely need some supplemental nigh time heat. When it's 80's here it's usually that temperature for several hours which heats everything up (ground temperatures, rocks, walls, etc...), which helps sustain favorable temperatures long after the sun goes down. Your temperatures sound like some cool winter days here, and it's not likely your tortoise will be able to elevate its body temperature long enough to sustain itself through the cool nights. This is just me guessing here, a better resource would be someone who keeps leopards in your area.
I think you are right. And I think this is a large part of why the things the might work in Phoenix, don't work elsewhere. The mornings warm up fast there and everything stays warm well into the night. We have similar highs for much of the year, but we don't get warm until much later in the day than you, and our nights get colder much faster. The sun goes down here and the jackets and sweaters come out right away. Heck, this time of year, the jackets come out before the sun even gets all the way down.