Heidegger and the Nazis

I was going to start this post with a stamp of irritation with BBC Radio 4 saying what Friday coming's Afternoon Play (Todtnauberg, by John Banville, which might be quite interesting) as presenting an account of a meeting between Paul Celan and Martin Heidegger, "the Nazi Philosopher."

I'm no fan of Heidegger, but, although it might be entirely fair ('cos it's true) that he was a Nazi, it's surely unfair to say that he was "the Nazi Philosopher." As Richard Rorty insists, surely we can separate the man's terrible politics and actions from his work (and our use of that work)?¹

But now I'm not so sure of that position: an internet search (oh font of verifiably high-quality wisdom!) brought this long paper to light (with a response here), where Alex Steiner argues that it is quite possible to associate Heidegger's work with his Nazism. I don't know enough to be sure. Is there anyone out there with a helpful opinion?

¹ Rorty addresses Heidegger's Nazism in in 'Another Possible World,' which was published in the London Review of Books in 1990. The essay was republished in Philosophy and Social Hope as 'On Heidegger's Nazism.'