A Rapoport effect is a pattern in which species' geographic range sizes increase toward the poles. Previous work suggested that Pleistocene glaciation caused the extinction of small-ranging species at higher latitudes, resulting in a Rapoport effect among North American mammals. If caused by glaciation, Rapoport effects should be apparent in Pleistocene Europe, where glaciers advanced relatively far south, but not in Asia, where glacial advance was much more limited. Variation in geographic range size in the fossil record of Cenozoic mammals of Europe was quantified, binning fossils into European land mammal ages. Next, the same was done for Cenozoic mammals of Asia, binning by Asian land mammal ages and China faunal ages. By requiring a minimum sample size of ten points to estimate range size, most time bins on either continent were too insufficiently sampled to assess Rapoport effects. A Rapoport effect was found for four of twelve European land mammal ages, but cooling was associated with only one Rapoport effect. A Rapoport effect was never recovered in Asia. After scrutinizing the evidence for North American Rapoport effects among fossil mammals, the overall evidence for glaciation driving Rapoport effects is scant. Support for glaciation causing Rapoport effects is questioned.