but i wonder if the size of the wire( primary and secondary) of the transformer should not be too small to give the 2/3 of the power even if the iron is OK!
Power is power..... amperage is amperage !!!
IN GENERAL; the core is determined by the the power
wire size is determined by the amperage
Both will determine temp rise but 5KW iron will will have no problem in the config Keith has described.
As long as the input voltage is near design value, in Amateur service, it should work just fine.