From what I've read about others' refrigerating habits, it's more important to keep "professional" film cold than mass-market consumer film (Ektar vs. Kodak Gold/Max, for example), since the latter is manufactured more toward long-term storage (and generally lower quality) than the former. Also, it's more important when you think you'll be keeping film past its expiration date; the cold helps keep the chemical changes that result in color shifts from happening, especially with slide film.
Personally I've seen Ektar stored in my local camera shop at room temperature and only slide films and bricks of print negative films stored in their fridge. I'd say you shouldn't have to worry about your roll of Ektar, but I have a spare fridge in my garage I specifically use for film, regardless of kind or age.
Most food and film comes wrapped or boxed, so cross-contamination shouldn't realistically be a concern. But if you want, put your film in a plastic bag or container. Just remove your film and allow it to come back up to room temperature before using.