Lily's safe travelling

Lily being hairless makes it hard to travel during high heat times I am looking for a way to travel with her during the day but keep her cool and safe I am looking for help with items that people know will work well with my bmx bike and or cart or just advice to keep her cool while we travel. I do need ice packs and a small cooler so I can put water in the cart and keep it cold for her. Thank you