While ideally Parmesan may be stored (at home) in refrigerated environment, there is no harm done to it (assuming nothing else like condensation occurs) by allowing it to sit at a warmer temperature for a few days. It is, after all, aged at ambient temperature for 2 years.
At least where I live, stores do not even put Parmesan in a refrigerated case; it is sold from tables at room temperature would would be slightly higher than what you measured in the shipping box.
I think your 18 C cheese should be just fine.
See also: How to store Parmesan cheese?