From what I've been reading about trout, you can legally keep trout in NJ if you get them from a hatchery. That's IF a hatchery will sell you individuals. If you take any from the wild, fishing regs DO matter, as you're taking a game fish from the wild. Nothing in NJ fishing regulations prohibit keeping trout and those fishing regulations actually do matter as it concerns a species that is regulated by your states fish and game department.
Concerning temps, everything I've read from other trout keepers says that rainbows are more tolerant of higher temps, although anything above 68 should probably be avoided if possible.
Anyways, this is all from what I've been reading. Get 'em from a hatchery if you can and you should be fine. If you ever feel uncomfortable, shoot an email to a local fish and game official. They'll answer your question and then you're covered.