Cardboard and liquids are not best friends so it is better to keep them apart as much as possible, perhaps in the cupboard or cabinet rather than out in the open if you are planning a lovely sauna.... Uhmm, sorry I meant shower.
There's some small potential for warping of the cap or base or even some colour transference if it gets wet, so if your new Woohoo is mistaken for a bath toy by one of the children perhaps just put it in a dry safe place until it recovers.
These deodorants will stay reasonably firm in higher temperatures up to 45 degrees, but please don't leave them in your car as they can melt and *may* leak.