A rigid carton protects the shape and an insulated container slows heat ingress, but both are limited against a long wait in a hot vehicle, so the box alone does not protect cream from the heat.
Manage the temperature risk separately from sliding and tipping: do not point the coolant straight at the cream, and set the cake base on a level, non-slip surface in the vehicle. Then trial the largest cake in its real box over the longest delivery.
