I breast and bottle feed my 4 week old. I pump once or twice a day if I have the time and give pumped milk in a bottle.

We are going out tonight for my birthday and I planned to bring a bottle of milk for the baby. I am planning on pumping before we go since fresh milk can be at room temp for 4 hours. However, if I don't have time to pump I do have frozen milk in the freezer. How do I go about storing this safely? Obviously I'll have to unthaw the milk before I go but once it's thawed what do I do? Can I keep it in a lunch bag with an ice pack and warm it up with hot water when he's ready to eat?