The trout's eye is not directly caused by the water temperature. However, most bacterial strains thrive in warmer water. Take columnaris for example, it is practically non existent in temperatures below 50' F. Ever been steelhead fishing in Erie in mid to late September, and seen the steelhead jumping out of the water in the mouths of the streams? That is a result of a bacterial infection like columnaris, or a parasite infestation such as Trichodina. The warm water also causes the fish the be stressed and allow it to become more susceptible to infection and disease.
In the case of the steelhead I used for an example, you have multiple factors that can allow for a fish to become sick. Warm water early in the fall, along with spawning stress can really hamper a salmonids ability to fight off infection. Now throw in a bunch of guys fishing for them in shallow creeks, and perhaps even being caught and handled, and you can see how a fish could become ill.