The problem with this seems to be that we can explain a bit about the physics of lightsabres based on first principles (more on this later), but no-one (that I know of) has ever explained exactly how adamantium is unmeltable/indestructable/unreshapable (apart from when Magneto decides to rip it from Wolverine's body).
I'm going to try to work this out using Universe Prime physics (ie. this one, according to DC comics...). Here goes:
Lightsabres (according to my thinking, I haven't looked any of this stuff up yet) must have three main components:
1. An extremely powerful but small heat source.
2. An appropriate substance (possibly a noble gas like neon) that can be released from the end and then heated by the above heat source into a plasma.
3. A highly localised electromagnetic field generator for keeping the plasma in a blade shape.
Given that phases go as:
solid -> liquid -> gas -> plasma
with temperature, then think of a plasma as being like a gas. This means that when lightsabres clash, it's not the plasmas bouncing off each other (as they would just pass straight through each other), but the highly localised electromagnetic fields bouncing off each other instead. This means that you should be able to hit lightsabres against each other even if their heat sources weren't working (so you wouldn't be able to see each blade, but you'd feel the collision of the fields).
Question then is, what would happen if you tried to shove a non-plasma-working lightsabre through a normal metal? In other words, would the field of the sabre (made by it's internal generator) be stronger than the intrinsic electric field of the metal (the one that's keeping it together in the first place)? Or in other other words, would the field of the sabre be able to push the metal atoms apart? I don't think it would since the intrinsic field of the metal must be huge compared to the artificial field. But I guess this is an area where we can make up whatever technology we want, so maybe it can be allowed.
If we go by the argument that adamantium's atoms (I'm assuming it's an alloy and consists of more than one type of atom) cannot be pushed apart by anything (given that it is 'indestructable'), then the non-plasma-working sabre could not generate a field high enough to do this.
But if it's possible for Magneto's magnetic field to move adamantium's atoms apart, then the sabre could go through.
But then again, if we only assume that Magneto's field is only moving the atoms around (so each one is still next to it's nearest neighbour) and not apart then the sabre could not go through.
But then again again, to be able to reshape the metal, you'd have to re-arrange the nearest neighbours. So if Magneto can reshape adamantium using a customised electomagnetic field, then the (ridiculously high) field of the sabre should be able to push them apart too.
Given that the field would have to be pretty strong to even keep the plasma in the right shape, I'm going to assume that it's of the same order as Magneto's powers, so it can push the nuclei apart.
So I'm going with:
Adamantium 0 - (non-plasma working) light sabre 1.
(assuming it's the type of adamantium that Magneto can reshape, if it's not then this round goes to the adamantium)
Now to add in the plasma (heating) part:
A plasma: A substance that has been heated past the gas phase to the point where the electrons, which normally orbit their respective nuclei, are able to move around the plasma's container freely.
A metal: A lattice of nuclei which each vibrate around a mean position, with a 'sea' (or plasma?) of electrons moving freely around inbetween them.
When you heat a metal you're making the nuclei vibrate more around their mean positions, and the melting point is when the vibrations are so large the the nuclei can move away from their nearest neighbours (so does that mean that a melting metal is technically a plasma? Never thought about it like that but it makes sense) thus destroying the lattice structure.
If we assume that adamantium doesn't have melting point, then this would mean that 'somehow' the atoms are able to be heated without the vibrations (movements away from the centre or mean point) becoming any bigger. Hence they always stay next to their nearest neighbours, and hence the heat would make no difference.
(As an aside, maybe you could explain this by saying that the heating process was 'somehow' exciting some other energy modes than the position ones. For example you could say that the heat was causing the adamantium nuclei to rotate around more, rather than move back-and-forth more. If you wanted to be really silly you could argue that adamantium nuclei have hyper-dimensional properties meaning that the heat does make them vibrate more, but in a dimension that we can't see. What the hell, why not say that this other dimension is time, and say that adamantium is the reverse-time version of itself much like electron are backwards-moving-in-time positrons?)
So that seems to be:
Adamantium 1 - Light-sabre 0
(on just the heating side of things.)
But the lightsabre wins overall since it just needs the electromagnetic field to do the work, and the hot plasma is just a spectator. (Again though, if it's adamantium that Magneto can't reshape then the adamantium wins overall).
And, to summarise, this is based on two main arguments:
1. The electromagnetic field of the sabre would have to be ridiculously high to be able to push apart the nuclei of a normal metal, but since Magneto can generate the kind of field that is strong enough to do this for adamantium, we can assume that the light-sabre can too.
2. The heating from the heat source into the plasma would have no effect on the vibrational positions of the adamantium nuclei, hence no melting could take place.
The thing about point 2 is that it would mean that adamantium would have a maximum possible temperature. In that once you reached the (invented by me) vibrational limit, it wouldn't be able to get any hotter, and the energy would have to go into one of the other modes (or other dimensions if you like that kind of thing).
Maybe you could say that the heat energy 'somehow' just goes into the electron sea, but this would mean that adamantium would then give off electromagnetic energy (eg light, infrared, microwaves, gamma rays, etc) as you heated it (as electrons give off em radiation as they move down from higher energy levels).
At a push you could say that the vibrational movement does become massive, but by some weird fluke this doesn't lead to lattice falling apart (as in it somehow vibrates between several different lattice shapes instead of the the nuclei being able to move freely). I guess this would mean that things would get 'interesting' when you throw in the electromagnetic field too, so from these assumptions you could say that the heat would help the blade to go through the adamantium.
Have I just accidentally added to the canon on how adamantium physics works? If so: yay me.
