The key to finding trout in any season is finding water of the appropriate temperatures. There are no hard & fast rules about the temperature of water a trout will feed in, but there are some loose guidelines to use. Every trout has it's optimum water temp where it's metabolism is highest & the fish are the most comfortable. These water temps tend to be:
-For browns & rainbows = 45 - 75 degrees Fahrenheit
-For brook trout = 45 - 65 degrees Fahrenheit
That doesn't mean that any of these trout won't feed outside of those ranges. These are just the basic temperature ranges where they are the most likely to feed. Water temps right in the middle of those ranges you can figure as ideal conditions.
As I said, no hard & fast rules here. You can catch a trout in 40 degree water or in 80 degree water - both are possible. This is because the trout will become conditioned to, or acclimated to, their environment. Trout in a cold mountain stream will feed at lower water temps than those in a slower, wider stream that flows through the base of a valley. Just use common sense & those temp ranges as a loose guide, adapted for the particular water you're fishing.
Sometimes you'll hear anglers say that the water is too warm to fish for trout - that you'll kill any trout you might catch. This is true, but only partially so. The biggest thing that kills trout is a lack of oxygen in the water (or pollution). Under most normal circumstances, as the water in a regular stream warms up it disperses its oxygen. The hotter the water gets, the faster it loses the oxygen. Trout need well oxygenated water to live, & without it they will suffocate. Catching a trout that happens to be living in water without a high amount of oxygen will kill it. It just so happens that this usually coincides with higher water temps. So water temp alone isn't the only element to the story. You might find trout in the hottest part of the summer, with water temps in the low 80's, living below a water fall, for example. Those fish have plenty of oxygen, but they will move slower because of the hotter water.
So back to our first question: where did all those trout go? Chances are, unless there's some kind of predator lurking around, they went to where the water temps (& oxygen) were most optimal for them, in addition to food & cover. Water temps are the key to finding trout.
You should note that the temperature of a stream is different up & down the water column, i.e. the water will be different temps at the bottom, the middle, & on top. Knowing the water temps throughout the entire depth of where you're fishing can help determine if the fish will be feeding on the bottom or not, for example. So if the water is cold, say 48 degrees, I'm betting it might be time to slowly drift a nymph on the bottom.
In the summer, you can almost bet that some trout have moved up into the tributaries. Take water temps readings everywhere you go - & go up the tribs until you find water that is in the temp ranges for trout to feed. Sometimes this is the only way to find trout. Using your stream thermometer will also tell you where hidden underwater springs, or other cool spots are. This is very important info. Remember where those places are as they will help you find trout all year long.
So many of us overlook water temps, myself included, but they are the key to successful angling. A stream thermometer is one of the most important pieces of fishing gear you can own. It can not only tell you where to fish, it can also tell you what approach you should use or how you should be fishing. Knowing the water temps can also tell you when & at what time of day you should be on the water, too.
If you're fishing & you don't know what the temperature of the water is around you, you're only gambling. Get yourself a good stream thermometer & use it every time. That alone will increase your odds of catching more trout than your selection of flies, the line you use, or almost anything else you can think of. You can't catch trout if they aren't where you're fishing.