Involved in the biosynthesis of polyamines which are thought to support the growth of thermophilic microorganisms under high-temperature conditions. It seems that long-chain and branched-chain of polyamines effectively stabilize DNA and RNA, respectively. Catalyzes the irreversible transfer of a propylamine group from the amino donor S-adenosylmethioninamine (decarboxy-AdoMet) to norspermidine, spermidine and norspermine to yield norspermine, thermospermine and caldopentamine, respectively. It can also synthesize sym-norspermidine (bis(3-aminopropyl)amine) from 1,3-diaminopropane with a very low activity. The biosynthesis of caldohexamine and caldoheptamine from caldopentamine has been also observed. norspermine + S-adenosyl 3-(methylsulfanyl)propylamine = caldopentamine + 2 H(+) + S-methyl-5'-thioadenosine norspermidine + S-adenosyl 3-(methylsulfanyl)propylamine = H(+) + norspermine + S-methyl-5'-thioadenosine S-adenosyl 3-(methylsulfanyl)propylamine + spermidine = H(+) + S-methyl-5'-thioadenosine + thermospermine Homodimer or homotetramer. Belongs to the spermidine/spermine synthase family.