For an ill person, it is permissible to use it without any hesitation.

There might have been grounds to argue that there is an issue with screwing and unscrewing the cap, similar to the discussion by Maran the Rema in his famous Responsum (Siman 119; also mentioned by the Taz and Magen Avraham in Siman 340) regarding a book that has drawings and letters on the edges of its pages. In practice, the use of such a book is permitted because it is similar to a “cup of joints” (Kos Shel Perakim)—a cup assembled from two parts, which is permitted to be assembled on Shabbat because it is designed for this and this is its normal manner of use. Similarly, regarding the aforementioned book, since it is meant to be opened and closed, even though letters are formed and erased through this action, it is nevertheless permitted because this is its normal manner of use. Furthermore, each letter is considered from the outset as erased and as if it were written in tiny fragments. For this reason, it is permissible to close and open the hot water bottle since this is its normal manner of use. The same applies to a baby bottle, where without screwing the nipple onto the narrow opening the baby would not be able to enjoy the contents of the bottle, and yet it is permitted because the vessel is pre-constructed in such a way that it is not considered as if one has assembled or disassembled anything.