I don't believe ANY battery should be inside an enclosure. All batteries can leak especially in warm humid conditions.
There is ALOT of allowable variation in accurite, the manufacturer allows 4ºF up or down from correct. If the unit is 100% functioning according to the manufacturer allows 86-94ºF if it is reading 90ºF. That maybe acceptable for some I don't feel it is.
The three I have owned only one was inside this. The other two were replaced by the manufacturer under the warrantee the worst was 3ºF more than the specs reading 7ºF high. When I set my thermostat accordingly I noticed it was wrong with my finger. I am not convinced the pet store dial types are worse than the accretes. I don't like seeing specs more than 2ºF up or down, I prefer 1ºF up or down. OP if you check the specs and cannot find what the accuracy range is (+/- 2ºF for example) DO NOT BUY IT! general rule of thumb.
Hydrofarm also does not list the specs they are also +/-4ºF and they have 3ºF of hysteresis. This means the most accurate you have is an 11ºF window. IMO you need ONE tool capable of measuring better than 2ºF window. Look at either a more accurate thermometer or a more accurate thermostat. Something should be close (a degree or two) of correct.