The purposes of this study are: to evaluate the effects (good and bad) that administering heated cisplatin into the chest and abdomen cavity following surgical resection has on malignant mesothelioma; to collect data on the toxicity of cisplatin given directly into the chest and abdomen, and the levels of the cisplatin in the body; to determine if this treatment method has the possibility of helping patients with pleural mesothelioma live longer; and to determine if this treatment method can help decrease the rate of local recurrence of mesothelioma.