dude no problem at all, trout evolved in places where temperatures are below freezing several months out of the year (alaska, canada, rockies, cascades), a they have not been watered down in the hatcheries long enough to evolve into a whole new warm water species. Where i live in bc, the few lakes they stock (most are wild fish) are stocked in fall, and the fish overwinter under the ice and are nice and healthy come spring and summer. honestly warm weather is far more of a concern, if water temps get above 65 the fish will be very stressed, over 70 and their dead

As long as they are conditioned to the water at a natural rate before stocking so they don't go into shock which is common practice in stocking. They usually run salt over the fish to calm them down before release. Trout wear a bacteria immune system on there skin so the cold allows those bacteria to live and when it warms up the bacteria that protect them weaken or die and other bacteria can infect the fish killing them.

depend where you are located. my self youst to live in north carolina and they would stock the rivers and I could still fish in the winter (below 32 deegres).

Trout like the cold but the stocked ones don't do good in Indiana in summer in small lakes down south here, it's better to keep them than let them go when it gets warmer because they won't make it when it gets hot.