Here are couple of excerpts from a review of Brunkhorst's book.
Reivewed by Matt F. Connell, Contemporary Political theory (2002)1, 242-244.
“During his exile in America Adorno produced with Horkheimer the text for which they are most famous: Dialectic of Enlightenment. In a critical move familiar from Habermas, Brunkhorst endorses their dark critique of totalizing enlightenment, but is keen to emphasize that it is open to correction, seeking to avoid what he sees as the pessimistic side of Adorno’s negative theological critique, witch runs the risk of going ‘along with Heidegger and a broad stream of conservative cultural criticism. Critical theory falls back upon a negative philosophy of the history of decay.’ (p. 75)”
“For me, Brunkhorst’s most extensive and valuable contribution is his attention to the complex of disputes on Adorno’s legacy in modern critical philosophy, a complex which forms the philosophical background to many of the issues of cultural theory. Different lines of theoretical relationship to Heidegger is crucial here, and Brunkhorst’s book is dominated by an effort to clarify Adorno’s complex theoretical relationship to Heideggerian thought, with Brunkhorst being careful to make clear the commonalities as well as the differences. Brunkhorst develops his analysis of Adorno and Heidegger into an interesting series of juxtapositions with post-modern, analytical and pragmatic schools of thought, carefully unpicking (sic) a range of affiliations which place aspects of Adorno close to pragmatism (especially Dewey) and postmodernism (especially Rorty), whilst being well aware of the areas of distance which are emphasized more strongly by other receptions of Adorno.”
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I think the reviewer is right in his claim that the heart of the book is Brunkhorst's elucidation of similarities and differences between Heidegger and Adorno (it goes without saying that the account is from the perspective of critical theory and not that of Heidegger or Heideggerians).