The OP made the comment that he installed two of these transformers, one at his house and one at a friends. Only one seems to have this issue. There is primary current flow all the time and secondary current only flows when a button is pressed. Since heat buildup would be the result of current flow, the only way to troubleshoot this would be with a AC current meter connected (clamped) on the primary side. Without this we are all guessing....
Take both transformers yours and your cousins out,
put them on a table with no load on there secoundarys
and monitor there temps,
you will soon see if there is a problem,
a faulty transformer will soon be too hot.