Like with all battery powered electronic devices, H2O-Pal's battery will be negatively affected if it is repeatedly exposed to freezing or near-freezing temperatures. We would suggest you do not put the device in the refrigerator (or if you do, then separate the tracker from the bottle at the magnetic connection and only put the bottle in the fridge).
If you can, a good option to keep water cold in the bottle is to put some ice into it.
Please make sure to NEVER put the H2OPal bottle in the freezer. As water expands when it freezes putting it in the freezer would likely break the bottle and that could be dangerous.