The purposes of this study are: to determine the feasibility of administering adjuvant cisplatin plus ALIMTA to patients who undergo surgery with heated cisplatin during surgery; to determine the effects (good and bad) of this combined modality approach in patients with mesothelioma; to evaluate cisplatin effects by determining where it goes and how it is excreted in the body from the collection of tissues and cisplatin samples; to collect and analyze discarded samples of mesothelioma tumor during surgery to help determine the genetic make-up of the disease.