Acting calm is easy eh, so why so many questions??

I would sub if it were me, considering your situation.

Yes, the heat pads work. No, they can't watch, which is why I recommend you sub. They'll make you empty out your pockets, not sure if pat-downs are legal; BurntToast would know more on that.

To avoid any stress with hiding it, my last test, I simply strapped the bottle to my upper thigh with an Ace bandage, and had the heat pad on the side facing out. It worked like a charm.

Hope this helps. I'm in no way an expert, but you just have to have a plan of action, practice, & stick to it.

Good luck! ~