Based on the high correlation between species richness in sigmodontine rodents and temperatures, we propose a new model in order to quantify past climates. Because of the close phylogenetic relationship and the tooth morphological similarity between extant New World cricetids (Sigmodontinae) and fossil European cricetids (Cricetinae s.l.), extant New World sigmodontines are taken as analogues for Old World fossil cricetines. Sigmodontine species richness has been compiled for 282 extant local faunas from North, Central and South America, with corresponding climatic data (temperatures and precipitations). There is almost no correlation between areas covered by local faunas (ranging from 1 km2 up to 46,000 km2) and numbers of sigmodontine species in localities (R2=0.027). Number of sigmodontine species in local faunas and mean annual daily temperatures are highly correlated (R2=0.88). The relationships of species richness and precipitation is low (R2=0.19 for mean annual precipitation). The method is exemplified for Old World cricetines using well documented Miocene rodent faunas located in the Lyon area.