Any ideas on how to clean carpet after feline distemper case?

Recently I got a kitten from the local shelter. He seemed really healthy and happy and then 3 days later I had to have him euthanized because he came down with a really bad strain of feline distemper. The shelter said he was up to date on his shots, but maybe he was exposed to it before he had a chance to build up his immunity. Anyway, the point is, I may want to get another cat in the future - who will be up to date on all his shots for sure before he's introduced into the environment - but I don't want to put any possible new pets into harm's way. Obviously no unvaccinated cats will be brought in as that would be pretty much a death sentence. Any ideas on how to clean the carpeting though? The apartment carpeting is light brown and apparently bleach or really high temperatures are the only thing that will kill this horrible bug, but I'm not sure if regular steam cleaning would be enough. Has anyone had this problem before? Thank you.