Sounds like a dodgy iron - a TC unit at a price that seems too good to be true, probably is!Yes the solder does sometimes go right up in smoke and burn rather immediately, however, I have adjusted the temperature dial and it helps some but the solder either burns or won't melt at all. I haven't found a sweet spot where it just works.
What is "eutectic" solder?
I am using thick solder right now and my components are quite small (GameBoy PCBs), what should I search for to find solder with a smaller gauge?
You can get a perfectly good uncontrolled iron at reasonable price - but you still have to watch out for crap.
The irons I use are Antex which I've had very little trouble with, I know they do them in both voltages, so it might be worth seeking one out wherever you are. AFAIK: they also do a 12V type.
Google can probably explain eutectic better than I can.