I was going to offer the same advice as Trof but, unfortunately, Saran wrap is poorly permeable to oxygen. You might want to shop around, though, as some clingfilms are gas permeable
(eg. http://shprema.en.al...ping_fresh.html )
In the past I have used similar clingfilm with good effect when Parafilm went too pliable, sticky/gunky at 37oC and 56oC.
You might just have to give some form of clingfilm a try and see if it suits your purposes.