Just imagine a (prismatic) block of material with crosssection A in a homogeneous gravitational field (so that the potential is m*g*h). It does not matter how it got there. If this blocks "moves down" by delta_h it releases the energy M*g*delta_h(1), where M is the mass of the total block, M=A*h*density(*). The question is now: is that released energy enough to melt the delta_h hight base layer of the block? It is if the energy equals H_m*A*delta_h*density(2), where H_m is the melting enthalpy of the material the block is made from and A*delta_h*density the mass of the layer that has to be melted. Equate (1) and (2) (and substitute (*) into (1)) and get: g*h=H_m. So, for h>H_m/g the lowest layer of the mountain melts away (and gets squeezed out) until the mountain reaches the critical height.
The equation (*) depends on the geometry of the mountain, it would be M=A*h*density/3 for a cone.
The height is measured in relation to the (floating) tectonic plate.