Yeah in my opinion those things are just a scam but I'm not a doctor so fuck if I know really lol. If your in the car or on a bus, as long as the bottle is tight to your body, your natural temperature should keep it warm.
There's an easy way around that, just say you have something on that day like looking after the kids until your partner comes home etc and ask would it be possible to do it in the afternoon, or vice versa if you would rather do it in the morning.
I normally go with "I have to bring my grandmother to her doctors appointment that morning, would it be possible to come in the afternoon?".....I don't even have a Grandmother lol. Obviously I did at one point in life but not for 15+ years and she was cool so I'd imagine she's alright with it haha.