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To my poor knowledge on the topic, the gravitational waves that are most likely to be detected by LIGO or other experiments do not have thermal spectrum. But I'm not certain.

I know that Hawking's radiation is thermal and it is partially make up of gravitational radiation. However, as far as I know (correct me), its detection is not possible in practice.

I think that the gravitational wave background is thermal, but I have no idea about its direct or indirect detection. Will (Advanced) LIGO be able to say anything about this? Maybe the B modes of CMB can tell us something?

Any information about possible sources of gravitational radiation with thermal spectrum will be welcome.

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Have a look at this arxiv.org/abs/0708.3343 –  anna v Aug 14 '12 at 3:20
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