Create a hi poly cube, take the sculpt polygon tool and start pressing the vertices down--see the resault.

Key is to take a lot of blends to control the melting realisticly.
But on every next blend shape press the brush on diferent place.
This way you'll have a lot more control of each phase of melting.

Another way is by using the softbody dynamics.
Lattices-particles-then use per particle attributes to control melting, try with ramp map and writting an expressions to control movments of particles.

You'll get a lot more controls by using per particle attributes then by using fields.

Try using 2 cubes, one wich will be deforming geometry and second,NURBS, wich will be used as a goalPP for particles wich will then deform a poly cube.That NURBS cube you can easly reshape and so affecting goal UV PPA.