European beech (Fagus sylvatica L.) forests in the Iberian Peninsula are a clear example of a temperate forest tree species at the rear edge of its large distribution area in Europe. The expected drier and warmer climate may alter tree growth and species distribution. Consequently, the peripheral populations will most likely be the most threatened ones. Four peripheral beech forests in the Iberian Peninsula were studied in order to assess the climate factors influencing tree growth for the last six decades. The analyses included an individual tree approach in order to detect not only the changes in the sensitivity to climate but also the potential size-mediated sensitivity to climate. Our results revealed a dominant influence of previous and current year summer on tree growth during the last six decades, although the analysis in two equally long periods unveiled changes and shifts in tree sensitivity to climate. The individual tree approach showed that those changes in tree response to climate are not size dependent in most of the cases. We observed a reduced negative effect of warmer winter temperatures at some sites and a generalized increased influence of previous year climatic conditions on current year tree growth. These results highlight the crucial role played by carryover effects and stored carbohydrates for future tree growth and species persistence.