Storage shouldn't be a hot place. Attic / loft storage may be a bad idea in the summer. Ditto garages / sheds. The key words are cool dry.
Are these pressed DVDs or did you record them yourself? "Some" DVD drives and software allow one to get an idea of how the errors are doing. This could allow you to copy the content before the error rate became too bad for the reading correction algorithm. Sorry, but I can't point you at specific drives or software. I see Plexstor in a hazy recollection.
seacue