thermodynamics - Difference between dissociation energy and dissociation temperature for water?

I was trying to find the temperature at which water dissociates into hydrogen and oxygen, and so I came across this Wikipedia page. It states that it takes 493.4 kJ/mol + 424.4 kJ/mol to dissociate the bonds in a water molecule which gives a total of about 920 kJ/mol or about 51 MJ/kg. So I tried to calculate the temperature that would give that huge amount of energy using the heat capacity of water vapor. I took 3.3 kJ/(kg K) for water vapor as an average specific heat, and so by simply dividing 51 MJ by 3.3 kJ, I ended up with about 15 000 K.

But on this other Wikipedia page, I found: "at 2200 °C about three percent of all H2O molecules are dissociated into various combinations of hydrogen and oxygen atoms. At the very high temperature of 3000 °C more than half of the water molecules are decomposed".

So now I am very confused. If 3000 °C is enough to dissociate more than half of the water molecules, then it should be expected that almost all the molecules should dissociate at around 4000 °C or so and not the 15 000 K I calculated earlier.

So am I missing something here? Or is there an explanation to this?