Catalyzes the transfer of a methyl group from trimethylamine to the corrinoid cofactor of MttC. Co(I)-[trimethylamine-specific corrinoid protein] + H(+) + trimethylamine = dimethylamine + methyl-Co(III)-[trimethylamine-specific corrinoid protein] One-carbon metabolism; methanogenesis from trimethylamine. Can form a complex with MttC. Belongs to the trimethylamine methyltransferase family.