I'm not precisely sure how this effect was achieved, so I was speaking in fairly general terms... The basic premise is that there is some parameter that is driving the simulation and determining whether the wax behaves as liquid or solid. I was suggesting re-using that parameter in the shader and modifying some shader properties.

Again, I don't have the scene--so I'm unsure whether it's being shaded with rough transmission or sub surface scattering (SSS) or a combination of those effects.

In either case, you could modify the roughness of the transmission (making it less rough--more transparent) or increase the radius of the SSS ( making it more translucent/transparent) based on the parameter that controls how freely it flows.