S-adenosyl-L-methionine-dependent methyltransferase that specifically methylates the C5 position of cytosine 72 in tRNA(Thr)(TGT) and tRNA(Cys)(GCA) (PubMed:26160102, PubMed:27703015, PubMed:28531330). In vitro also methylates tRNA(Thr)(AGT) (PubMed:26160102, PubMed:27703015). Methylation requires, in the acceptor stem region, the presence of the 3′-CCA terminus, the target site C72, the discriminator base U73, and the second and third base pairs (2:71 and 3:70) in the tRNA substrates (PubMed:26160102, PubMed:27703015).