I am an experienced nursing mom- and I am very comfortable nursing in public, so I recommend that first. The mall can be intimidating...it can be hard finding a private space. I know some "upper scale" malls have nursing rooms- which are really nice. Most maternity stores will lend you a dressing room. I've used dressing/changing rooms in larger stores (Dillards, Foleys, etc). Larger department stores may have a "sitting" area in the restrooms- not a stall! You can sometimes find a bookstore with seating that is private (Barnes and Nobles, Borders, etc). Also in food court areas, if you avoid lunch time, you can find a corner seat and face the wall- your back is towards the public.
But for bottle temp, I have always warmed it to room temp. Since breastmilk is good for several hours (depending on environment) you don't even need a cooler pak.