Hope some of this helps you Becky???
I water all my herbs with tepid water, not cold.
The rosemary I have is in a large pot in the garden and I don't bring it in, it just survives whatever the weather. I only water it once a week, a drenching lol in the warm months, and don't water it at all in winter. However, I regularly snip the top of the stems off to encourage new growth. Have just been out to double-check, and yes, mine has shrivelled and dried out base parts which I just clip off occasionally.
Try watering it just every other day - perhaps she doesn't like a constant heat???
Love and Hugs
ST
xxx