Abstract Aim Climate change has far-reaching effects on species and ecosystems. The aims of this study were to determine how climate factors affect the growth pattern of indigenous and exotic trees in Zambia and to predict tree growth responses to a warmer climate with the use of mathematical models. Location Two savanna sites in central Zambia. Methods Diameter at breast height (1.3 m above ground, d.b.h.) of 91 permanently marked trees belonging to three indigenous and four exotic species was measured fortnightly for periods of 1–2 years from 1998 to 2003. Correlation and regression analysis was used to determine the effect of climate factors (minimum, maximum and average temperature and rainfall) on monthly daily d.b.h. increment of each species. Regression models were used to predict the growth behaviour of trees under a 0.5 °C warmer climate. Results Interactions between temperature and rainfall explained 60–98% of the variation in d.b.h. increment in all the tree species, except the exotic Eucalyptus grandis. For deciduous species, stem expansion was delayed by 2–12 weeks following leaf-flush and d.b.h. increment peaked during the rainy season. Evergreen and deciduous species could not be separated on the basis of annual d.b.h. increment because the higher growth rates of deciduous species compensated for the shorter growing period. Mathematical models predicted slight changes in d.b.h. growth pattern under a 0.5 °C warmer climate in five of the seven species. Significant changes in d.b.h. growth patterns were predicted in the indigenous Bridelia micrantha and exotic Gmelina arborea under a warmer climate. However, models failed to adequately represent potential soil water stress that might result from changes in tree growth patterns and a warmer climate. Main conclusions Climate factors explained a large proportion of the variation in diameter growth of both indigenous and exotic trees, rendering it possible to model tree growth patterns from climate data. Tree growth models suggest that a rise in temperature of 0.5 °C is unlikely to induce significant changes in the growth behaviour of the majority of the studied species. However, because the growth behaviour of some species may be substantially affected by climate change, it is recommended that strategies for the future production of such climate-sensitive trees should incorporate aspects of climate change.