Your argument (large temperature leads to greater mixing) is correct so long as there are no other large scale forces acting on the system. This isn't true in planet formation, because gravity plays a very important role.
I'm not an expert on planet formation, but I think the argument goes something like this: As a planet forms from material from the protoplanetary disc it will begin very homogenous, something like an asteroid, just rock and metal all the way through. If the planet is heated enough in the core, some material will melt. Buoyancy (due to gravity) will drive lighter material "higher" in the planet, away from the core. The more heat you generate the more melting can happen and the more material will start to separate by density.
Of course, there's a lot more to the story. Fluid material obeys the laws of hydrodynamics, so large scale convective flows can form in some regions, mixing those areas quite well. Planetary rotation adds centrifugal and Coriolis forces to the mix, which pull more material to the equator. The surface of a planet is exposed to space and can radiate excess heat, cooling to a solid (like the Earth's crust). If the core is magnetic and rotating, metals in the planet may be pushed by the magnetic field.
All this is just to say that planetary formation is a balancing act of a lot of competing forces. These forces can differentiate (or not!) different types of material, but first (for rocky planets at least) they need to be freed by internal heating.