At which temperature Parmesan cheese must be transported?
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?