Skiddaw Metamorphic Aureole part 1

We went up Mungrisdale Common by way of Sinen Gill. A granite intrusion breaks the surface in the gill and is surrounded by the well-known Skiddaw Metamorphic Aureole. The Skiddaw Slate has been changed by the heat of the magma welling up. This is contact metamorphism. In the distance in this photograph is another gill where we first found evidence of metamorphism. It is about 1km away. I looked up the temperature of magma and perhaps 1000 degrees Celsius would be a ball park figure. I was wondering about modelling the conduction of the heat from the magma through the slate. From https://en.wikipedia.org/wiki/Thermal_conduction heat flux density q=-k.(temperature gradient). So temperature gradient is likely to be of the order of 1 degree Celsius per metre. A value for the thermal conductivity of slate is 2W/mK. Of course, that is roofing slate so it isn't the same thing. But it would give a heat flux density of the order of 2000W per square metre.