Ice packs in the box. A lot of food subscription delivery service packages look like this. The inside has an extra layer of thicker paper to resist condensation

The fancy ones use dry ice instead of regular

Judging by the medications I've received, it's probably a much smaller cheesecake than that box suggests, and is still icy cold, if not fully frozen. Packed in layers of ice packs and sealed in a thick Styrofoam box. OP has at least another 24 hours to find the recipient, longer if they put the whole box in their fridge. They could also remove just the cheesecake and refrigerate it, while checking the packing slip for more information, but they would need supreme willpower.

It’s a cheese cake from Junior’s. They’re packed with dry ice.