To avoid any issues at the airport, i always activate my Frio at the destination before going out for a walk in the heat of the day.
I keep my insulin insulated with a sweater in my hand luggage. Airplanes and coaches have never been very hot as they are usually air conditioned and insulin is fine up to 30 degrees.
In an emergency, I have soaked a Frio in a cup of water by rolling it up. I have never needed a towel. My Frio are old but they came with cases that protect anything from the water.
I have a work trip to Dubai next week. As I will be in or transitioning between air-conditioning all the time, I will not be bothering with Frio.