Agreed. Nomatter what the temperature, if you have a fish out of water for too long as described, especially after a 5 minute fight, then water temperature is not the reason that its going to die.
Anytime you need to "revive" a fish is a bad sign. The fish may seem as if its revived, and swim off looking apparantly fine. But there's a good chance that fish is going to die from acidosis within a few days.
Biologically speaking, trout are similar to humans in their metabolism. Muscles need energy to move, which is usually supplied by aerobic metabolism (requires oxygen and sugar to create energy). But we have systems for anabolic metabolism too. This occurs when there is not enough oxygen, either from lack of actual oxygen available or strenuous exercise which exceeds the heart and arteries' ability to transport oxygen to the muscle. Anabolic metabolism does supply the energy required to do the job, however a side effect is hydrogen ions being produced, which lower the pH, i.e. acidosis. It's why we get sore muscles, for instance. And like sore muscles, the peak effects are often a day or so later. And in order to recover, you must consume more oxygen at rest than is otherwise typical.
All the same is true in fish. If we have an extended fight, the fish is undergoing anabolic metabolism to supply its energy, and moreso if the water is warm and the available oxygen low. Holding it out of the water requires more anabolic metabolism just to keep the fish's organs functioning. And upon release, that fish needs more oxygen to survive than it did prior to being hooked. If that oxygen isn't available, more anabolic metabolism will take place, until the blood is acidic enough to kill some of the organs in the fish and the fish dies.
Bottom line: The warmer the water, the shorter the fight and quicker the release must be for the fish to survive. In water that remains above 70 degrees for any length of time, there is very little leeway for any fight or release to take place, and the fish is unlikely to recover due to lack of oxygen in the hours and days AFTER the fight. Just because it looks fine when it swims away does not mean it will live. But if that same fish swims away fine in the warmer water, and the water overnight cools to more comfortable levels, enough oxygen may be available for the fish to rest and recover from its ordeal.