I think it depends on several factors, but IME, I've always liked to hunt any time I get a chance. This whole moon phase, weather, is just all crap. Elk don't disappear when the moon is full, the weather is hot, windy. I think lots of people just look for excuses not to go and reasons why they fail. If I had to wait for the "perfect" moon phase, perfect weather, etc. etc. I probably wouldn't get a chance to hunt more than a couple days a year.
I found this raghorn in early September and watched him fight another bull just a little smaller, and take 20 or so cows with him. I shot just over the bull he fought. I had to head to work and a friend saw him again on about the 8th of September and he had lost all but a couple cows. I got back from work and on the 13th of September and made a run at a different bull right at daylight. That bull was a very heavy old 6 point, probably in that 340 range. It didn't work out. About 10 AM or so, while walking back to the truck with my Dad and Brother...heard a bull bugle. It bugled again and sounded much closer and moving uphill toward us. We didn't call, just let the bull keep coming. I finally got a glimpse of him at about 100 yards, working up the edge of some heavy lodgepoles. He walked just slightly past us and I arrowed him at 30 yards and ended up being the bull I had seen fight about 10 days prior.
Point being, I couldn't tell you what the moon phase was, couldn't tell you what the temperature was, don't really care and never have. IME, the best time to hunt is every chance you get...and being in the woods all day increases odds even more.
Said raghorn:
Another look: