I’m not sure I would to be honest
It sounds like somebody’s damaged their hot water bottle from doing that
I had a cooling pet mat 😂 you just keep it in the fridge. Also, I used to travel on the tube with a flat frozen water bottle. Do you know what I mean, the kind that you can roll up when it’s empty? If you have to commute when it’s boiling hot, you can actually be a bit discreet keeping that between your back and the seat, lol.
Although if anyone spots you, they will inevitably say “ oh my God, that’s a brilliant idea” 😂