To put it briefly, I have no idea. There doesn't seem to be a lot of information around on this, but I found a couple of references.
I had a look in Caldwell's "Mastering Artisan Cheesemaking". Nothing specific there, but a passing reference that she aims to keep her cave between 50 and 55F (10-13C).
I also found a reference on the
cheesemaking.com website which suggests that the temperature should be set in the range 52-55F.
These two references seem to indicate an acceptable range of between 3 and 5 degrees for the average temperature, so perhaps a swing of a similar range would be acceptable. (My own guess would be that the swing is actually less critical than the average temperature and that humidity is a more important variable.)
A nice piece of research on your part though.