Laura Lu, Your insulin should fare just fine for your eight hour flight. Keeping it in your hand luggage is smart. The planes are kept at a comfortable temp for insulin. Refrigerate it when you arrive and you will be just fine.
If you feel so inclined you can get freezer packs, but you will have to do some fancy explaining at the gate. Usually, you can get your packs through the inspection if you have adequate reason. KGM managed to get her freezer packs through hand luggage inspection by claiming she needed to keep her insulin cool. All they can do is make you throw it out.