We took an Alaska cruise in June of 2022 and also found that the Dining Room was fine temp wise.
For the first time on any cruise, I packed leggings that were lined for during the day and a few nice looking down vests for outings. The vests came in handy with zipper pockets during the day for my room card, etc. I also always wear a dress to dinner no matter where we are cruising, just makes it feel more special while dining in the main dining room. An Alaska cruise is more casual during the day than other cruises, just be comfortable.