Variable wattage vs temp control in a soldering iron?
I suggest you get a Metcal , used ones are available. 
No bell no whistle , just an on off switch. I use only 
two tips ; a small pointy one , and a bigger broad one.
The Metcal heats up in a few seconds and can solder 
surprisingly thick heavy metal objects as well as tiny leads,
and traces .
  Use a small blob of melted solder on the tip to transfer heat
to the joint being soldered - this helps the heating tremendously.
Remove the heat source the moment the joint shines with shiny flowing molten liquidity , but without moving the joint , or you may get a “cold solder” joint .