Many palaeoclimate estimates are based on the climatic ranges of the nearest living relatives (NLRs) of fossils. If the climatic ranges of the true NLRs of the taxa in a fossil assemblage do not overlap, then the past climatic ranges of some of the fossil taxa are different from the ranges of their NLRs. Discrepancies between the climatic ranges of the inferred NLRs of co-occurring fossils are common, particularly in assemblages older than the Middle Pleistocene. Evidence from Early Pleistocene Tasmania indicates that many anomalies are caused by extinct species, or at least extinct genotypes. It is likely that pre-Quaternary fossil deposits will contain more extinct taxa. Most of the extinct Early Pleistocene taxa have warm climate NLRs, but they appear to have occurred in climates no warmer than modern climates in western Tasmania. Sometimes NLR approaches in climate reconstruction appear to be biased by extinctions of ecotypes and species, especially ones caused by the Pleistocene glacial-interglacial cycles. Extinctions also mean that it is difficult to identify palaeoclimates that are different from any modern climate.