Soldering iron temperatures
I'm going to follow up what Some Hardware Guy had to say - your problem may not be one of too little wattage, it may be one of too little mass at the heated tip. The greater the tip's mass, the more thermal inertia it has; a tiny tip cools off very rapidly, while a larger time cools off more slowly. I have a 15W iron out in the shop that's so massive that it'd burn a hole right through a PC board. Takes a very long time to get it up to temperature, but desoldering parts with it is really really easy because no amount of solder on a PC board will cool it below solder's melting temperature.

That's really the crux of the problem. When solder goes through a change from solid phase to liquid phase, that phase transition requires far more energy than just heating it to the phase-change temperature... then it releases all that energy again as it shifts from liquid phase back to solid phase. Your iron needs enough mass to cross the phase change barrier.