Summary Climate warming is causing compositional changes in Andean tropical montane forests (TMFs). These shifts are hypothesised to result from differential responses to warming of cold‐ and warm‐affiliated species, with the former experiencing mortality and the latter migrating upslope. The thermal acclimation potential of Andean TMFs remains unknown. Along a 2000 m Andean altitudinal gradient, we planted individuals of cold‐ and warm‐affiliated species (under common soil and irrigation), exposing them to the hot and cold extremes of their thermal niches, respectively. We measured the response of net photosynthesis (Anet), photosynthetic capacity and leaf dark respiration (Rdark) to warming/cooling, 5 months after planting. In all species, Anet and photosynthetic capacity at 25°C were highest when growing at growth temperatures (Tg) closest to their thermal means, declining with warming and cooling in cold‐affiliated and warm‐affiliated species, respectively. When expressed at Tg, photosynthetic capacity and Rdark remained unchanged in cold‐affiliated species, but the latter decreased in warm‐affiliated counterparts. Rdark at 25°C increased with temperature in all species, but remained unchanged when expressed at Tg. Both species groups acclimated to temperature, but only warm‐affiliated species decreased Rdark to photosynthetic capacity ratio at Tg as temperature increased. This could confer them a competitive advantage under future warming.