I've got a wireless indoor/outdoor thermometer. When we had a problem with our 'frost free' freezer not really getting cold enough*, putting the outdoor unit in the freezer meant we could monitor the temp from another room.
Works fine and you can tell if the battery has gone flat because the reading disappears altogether.
*This is a common problem caused when overpacking blocks the airflow that is necessary for the frost free to work. We were on the verge of buying a replacement, but as we were away for a weekend we decided as a last go to use up as much of the contents as possible then left it switched off for 48 hours (with a towel on the floor).It's been as good as new since then.