Well, a fire requires a rupture of tanks/fuel lines and a source of ignition.
The hot engines appear to have detached, so are far from any leaking fuel, and the wings seem to be fairly intact, so there was no misted fuel to ignite easily and then spread to pools of fuel. In addition, the ploughed field is ideal for soaking up leaks and making it much harder to ignite. It also has the useful property of being soft and so absorbing impact forces, which helps to reduce deceleration injuries.
@DaveReid
I saw the small areas of damage you mentioned, and seeing the condition of the rest of the fuselage I'd guess it would be the frames of the cockpit bukhead being pushed upwards as the fuselage distorted from below, rupturing the top skin. Or maybe the structure around any galleys/toilets aft of the cockpit.
Make sense?