In the heat of summer many trout will be relatively inactive during the hottest hours of the day. If you're trying to catch them, you obviously stand a better chance if the trout are feeding. During the hottest times of the year trout tend to feed more in the wee hours of the morning, like say from 2 or 3 am & on until after sunrise until maybe 8 or 10 am in the morning, depending on conditions.
Another reason to consider fly fishing at night is because once a trout reaches a certain size, maybe 22" & up, they stop eating as many insects because bugs don't provide enough nourishment to keep them going. Instead, these big lunkers turn into predators & eat thinks like other fish, baby ducks, mice, & anything else of substantial size in the water. They are hunters & they do their best hunting at night. A really big hatch will still bring them out in the daylight - even if to eat the smaller fish who are distracted by the hatch. Usually though, these big monsters rule the night in the stream.
So if you want to have more action & improve your chances of catching the biggest trout in the stream, then night time is the right time in the hot summer for fly fishing. To that end, you might want to give it some thought before you march out into the dark oblivion, fly rod in hand.
-Know the stream you'll be fishing & know it well. This is not only to improve your odds of catching a fish, but for your safety. It's good to know where all the rocks, logs, & pot holes are when you're walking or wading in the dark.
-Take someone with you or tell someone where you'll be. You wouldn't be the first angler to get stuck in the stream at night. Mud & quicksand are real dangers to take seriously.
-Take a flashlight with you, but use it as little as possible. You'll see your surroundings better when your eyes get adjusted to the darkness. Constant use of a flashlight will not only spook the fish, it will never let your eyes fully adjust to the darkness.
-Make sure night fishing is legal where you're going. On many special regulation waters it isn't.
I can tell you from my own personal experience that the biggest tugs I've ever felt on my rod & line along a trout stream have happened at night in the pre-dawn hours, usually from 3 to 5 am. It was that thrill that kept me coming back at night, although it can wreck havoc with your schedule. I just hit the coffee pot a little harder than normal in the afternoons. You can be almost guaranteed to have the stream all to your self at those hours, too. Because of all these reasons fly fishing in the middle of the night can be fun, dangerous, & addictive.