I used to always fuss about the VSL temperature, and I still do if it would otherwise get hot. If you've got ice or cold packs you need to tell TSA you've got "medical liquids." I prefer regular ice in ziplock bags so I don't need to carry it home. At a hotel I sometimes just use the ice bucket in the room.
VSL is fine for up to a week at room temperature, if you trust that your pharmacy has kept it cool.