Is it possible for the enemies of the Wall (wildlings etc) to light a fire so big that it will melt the Wall?
Let's run the numbers:
- The wall is 700 feet high = 213 meters
- On its top, 12 knights can ride abreast and it's wider at the base. Let's say that's 25 meters wide at the top and 75 at the base, so 50 on average.
- It takes 334 kilojoules to melt 1kg of ice (if it's at 0 degrees C to begin with, but the melting energy is large compared to what it takes to heat up).
- Oak wood yields about 15 megajoules per kg when burned
- An oak tree weighs about 14 tonnes
- A 100m section of wall would contain about 213*50*100*1000 = about 1 billion kg of ice.
- Burning 1 kg of wood can melt (at 70% efficiency) about 30 kg of ice.
- Which means you'd need to burn about 2500 fully grown trees
In practice, efficiency would be lower, but you wouldn't need to melt the entire wall section to make it collapse. OTOH, the melting water as well as partial collapses would tend to extinguish the fire.
Given a force of many thousands of wildlings, as well as giants and Mammoths, it seems doable. But it would be a massive effort requiring many days, and giving the Night's Watch ample warning (via a gigantic smoke cloud, even if there were no patrols) and time for countermeasures.
Simply digging a tunnel would seem to be an easier and quicker alternative.
It should be. In the very first sentences of the first book GRRM writes that the wall "was weeping", that is, it was dropping water from the ice. This means that during the Great Summer the ambient temperature is really near to the water melting point (0C).
A different question is if the Night Watch would allow it.
A third point would be that melting the wall in part will cause water enough to kill the fire!
With the release of the latest episode, the answer now appears to be yes.
In Season 7, Episode 7, with the help of an undead dragon, the wall has been melted.
The discussion on if the dragon was breathing fire is discussed below.
One plausible counter argument you could make, is that fire didn't destroy the wall, but rather the magic of the Dragon Fire and/or Night King himself. The wall was created by magic (the details are uncertain), and you could argue it takes magic to destroy magic.
Yes, no, but.
There are good answers on if it, as it stands, would be feasible. One point though is that a ice-construction like the wall would not remain with that shape. Put simply it would become more like a big heap of ice as the weight of the wall forces the construction to widen making it a slope of ice rather then a wall. A big one, but still.
From what I know there is no maintenance crew making sure the walls are steep etc. so in other words other forces has to be at work for it even to be standing as it is. As such once have to take into account that the wall itself is under some sort of protection or time-warp-anomaly.
By which the melting by fire also might prove futile.
There are tunnels through the wall so we know that the wall isnt indestructable.
So, if the wildings could get enough raw material ( Wood, oil etc ) to the wall and they could light a fire and keep it going for a few days they could start making dents in the wall. I dont think that the entire wall could be melted but a hole through a wall could deff be done if done in secrecy.
Most of the rangers are dead. Only 3 forts on the wall are operable ( barely ) and the Black Brothers are very few in numbers.