So I thought to myself, wait a minute, we don't even do this in real life (Middle East, a few other places excepted). Why would dwarves do it? And then I said to myself, well, because they have access to magma. Strictly speaking, if we were to try to do this with wood, it'd be incredibly inefficient. And here's why:
According to my back-of-the-envelope number crunching, it takes 2.57 MJ/liter of water to raise water from 23 C to 100 C and to boil it all off completely.
If we look up wood burning energetics, we see that a value of 30000MJ/cord ( slightly biased source:woodheat.org) for hardwood isn't far off. Note that things like pine would give off less heat. 30000MJ/cord is about 4220.7 MJ/m^3. If we take a chunk of wood the size of a liter of water, 1000 cm^3, and completely burn it, we would get 42.27 MJ out of it. So assuming we have perfect efficiency (WHOA HORRIBLE ASSUMPTION) it would require .061 blocks of wood at 1000 cc's to boil one liter of water. So we'd need a block of wood a quarter the size of a quart of water to get one gallon of water out of the system. IF everything was ideal.
So the 30GJ number for the wood was for perfectly dried wood in a bomb combustion chamber (filled with oxygen for better combustion). Unless your dwarves were seasoning their wood for several years in a sheltered location, and then burn the wood in an oxygen-rich environment, the numbers they'll get out will be much less. New wood has tons of water, so it has to boil that water off as well as combust, meaning less energy out. So let's say that our actual number is 1/4 of 30 MJ, taking into account the various types of non-hardwoods (tower-caps, for instance) that we're burning. So now we need a block of wood the size of a quart of water to boil a gallon of water.
Of course, when we're burning this wood, not all of this heat is going into the water. Far from it. Depending on the quality of the stove, anywhere from 70-90% of that heat is getting radiated away into the surroundings, regardless of the quality of the wood. So if our stove was 20% efficient in burning wood, a significant accomplishment, then we'd be burning a gallon and a quart of water-sized amount of wood to boil one gallon of water.
Add in other inefficiencies, like loss of steam and other thermal factors, and we can quickly see the amount of wood we need going up and up.
Post summary in one line: use magma instead.
Sorry if any of my numbers are off, I'm not a thermo guy. It's interesting to note that you'd need magma in order to boil this saltwater, so you'd have to pick your biome carefully. A volcanic coast line?