I struggle with this daily as I live in Africa and dd is milk anaphylactic. I think the thing to remember is that 25 degrees is actually quite warm and you don't have to keep it ice cold. I bought a small, soft lunch bag thing from M&S which is made of soft cool box material and I just keep them in there.
blameit Africa It was 28.5°c here today Inside of coolbag seemed warm as did bag with allergy meds in which was inside. Perhaps it is that the coolbag has seen better days. TBH your right though doubt the actual inside was 25°.
but insulation will only slow down the time it takes to warm up. These pens are quite light so presumably need very little energy to get in to change their temperature. It might work for a short time if you were carrying it from one cool place to another.
Inside of a car gets very hot in the sun so will be a special problem.