Recent success in the amplification of ancient DNA (aDNA) from fossil humans has led to calls for further tests to be carried out on similar material. However, there has been little systematic research on the survival of DNA in the fossil record, even though the environment of the fossil is known to be of paramount importance for the survival of biomolecules over archaeological and geological timescales. A better understanding of aDNA survival would enable research to focus on material with greater chances of successful amplification, thus preventing the unnecessary loss of material and valuable researcher time. We argue that the thermal history of a fossil is a key parameter for the survival of biomolecules. The thermal history of a number of northwest European Neanderthal cave sites is reconstructed here and they are ranked in terms of the relative likelihood of aDNA survival at the sites, under the assumption that DNA depurination is the principal mechanism of degradation. The claims of aDNA amplification from material found at Lake Mungo, Australia, are also considered in the light of the thermal history of this site.