The key thing is that the mesh has very little affect on the casing temperature, because it is much lower mass, so its time constant does not matter.
"so its time constant does not matter" This is pure assumption.
The long time constant appears only when the mesh is active ....not when it is inactive,
Same tiny 23g mass in both cases
The time constant does matter... but it is not related to the mass of the mesh.
There is something in the mesh other than 23g of mass causing the long time constant.
The amount of energy stored in the mesh should cause it to vaporise... but it doesnt