Although you can get millions for a successfully litigated Mesothelioma claim, you shouldn't assume that it will happen. First off, some states cap maximum payouts for asbestos-related claims, and even if you get a large settlement, you may not get it if the money runs out.
If you're concerned about past asbestos exposure and your prospects for getting Mesothelioma, you can contact the National Institute for Occupational Safety and Health (NIOSH) for more information. They're online at http://www.cdc.gov/niosh/.