Idea

and whats the idea. BTW, 100mOhm at 6V i would expect 60A, but your mosfet is to small to pull it down. 60A @100mOhm are 360Watt, whats that for a soldering iron? Normal for a 50Watt one is a resistance hundred times higher. Anyway, what is the idea behind this double modulated iron?

I want to make it more efficient than the one I currently have. The 100mOhm was just signifying a short. My soldering iron uses 115VAC and rated for 60 watts. I'll update that. And the voltage for this circuit is meant for a 12V battery which I'll update that too to not confuse or compicate things.

Then again, I don't need to complicate this and just use a Triac and a pot.

1.) The efficient does not increase with double modulation. 2.) 100mOhm as short, why a short?? 3.) Ok, yours is 115VAC 60Watt, P=V²/R -> R=V²/P -> R= 115V²/60Watt=220Ohm because metalls do have a positive temperatur coefficient PTC it might have an cold resistance of below 200 Ohm but not much. 4.) 12V battery, thats ok. You cant get 60Watt from 12V with most soldering irons on the market, cuz the resistance is made for 24V to get 55Watt in most versions i saw, but you might get around 15Watt with 12V. 5.) If you use a triac and a pot (plus a cap) you loose the nice blinky indicator which shows you how active the heating process is currently. A low clocked PWM around 2Hz is ideal to power a soldering iron.

Sadly, active loads cannot be made more efficient, when the requirement is to extract and use their heat. Their inefficiency is what make them heat up. If you want to adjust the temperature, you can use a low frequency PWM (as soldering irons have a very high time constant), and perhaps some sort of a temperature sensor. If you want to use a DC iron, a MOSFET is a good idea. If you want to use an AC iron - triacs. Also keep in mind, that it is good to have some sort of feedback that helps adjust the temperature because when you solder something down, you extract some of the heat from the iron, and without any negative feedback to compensate the PWM, the temperature may vary. This is easy to do - as hurz mentioned metals have a positive temperature coefficient. Just find some tungsten wire and wound a second winding on the same core as the heating filament. Then make a very simple circuit which measures a voltage drop across the tungsten winding. Use the error voltage to control the PWM.

Alternatively, you can use the same primary winding to measure its voltage drop, but since the wire heats before the core, and we want to measure the core temperature, the end result may be a faulty reading.