i presume you are referring to Star Wars,
the Death Star is just a chunk of metal (rather like a big satellite) so I wouldn't expect any drastic climatic changes on Endor after Episode VI. After the Death Star blew up I would deem it dangerous to be still on the planet due to bits of metallic fragments floating around and hitting Endor in a comet-like fashion.
Ironically one of Saturn's moons photographed three years after the first Star Wars film came out bears striking resemblance to the series most beloved enemy base