Adamantium does seem susceptible to heat in FoX-Men since Silver Samurai was able to use a superheated adamantium katana to slice Wolverine's claws. Granted, the science is a bit bs here, but this is a comic book film.
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The entire point of the presentation of what you're describing was that adamantium was the only thing capable of cutting adamantium.
This is an explicit X-Men series fact, as the only other occasion adamantium was pierced or damaged came in Origins: Wolverine, when Stryker shot Wolverine in the forehead with an adamantium bullet.
Moving on...
The very nature of this forum's rules mean lightsabers can only damage adamantium if they've damaged something proven to be as strong. They haven't. Therefore they can't. These are the absolute basics.
In comparison to what Grievous could do to him, Wolverine has taken far worse damage without his adamantium skeleton and continued fighting unimpeded. That's not a fabrication, it's not an exaggeration, it's not a bias interpretation - it's a fact.
If Grievous is close enough to strike Wolverine - with blows that, simply put, couldn't possibly incapacitate him based on actual evidence - he's close enough to get ripped to shreds. And Wolverine absolutely could rip him to shreds.
Wolverine, 10/10.
Wolverine should take this but sweet baby Jesus he'd be suffering. Imagine how much flesh would be burn/shaved off him from Grievous trying to cut him?
"Money and muscle, that’s what I want; to be able to do any damned thing I want and get away with it. Money won’t do that altogether, because if a man is a weakling, all the money in the world won’t enable him to soak an enemy himself; on the other hand, unless he has money he may not be able to get away with it."
Robert E. Howard