My advice would be to use a pump to remove all the air from the sections. While they collapse, fold them up into the GRP carrier section (where they are attached) and secure them with ratchet straps or similar covered with pipe lagging or another soft material. Tie in the cone ends with soft rope running loops. It removes all the issues with heat, altitude and flapping. It also makes for a much more manageable package on the road.
In this job, an electric pump is your best friend!