I’ve just ordered another pen from them. Their website says their packaging is designed to stay cold for 48 hours and can usually be used within the manufacture’s guidelines if a delay in delivery of less than 48 hrs.
Ive had a couple of deliveries where the ice packs were melted by the time I unpacked them, but they still felt cool. I’ve kept the packs to use for other things (fab for picnics or transporting food from supermarkets in hot weather), and they never feel warm, even when stored in a normal room. So I wouldn’t worry.