Rising temperatures and pronounced drought are significantly affecting biodiversity worldwide and reducing yields and quality of Brassica crops. To elucidate the mechanisms of tolerance, 33 kale accessions (B. oleracea var. acephala) were evaluated for individual (osmotic and elevated temperature stress) and combined stress (osmotic + temperature). Using root growth, biomass and proline content as reliable markers, accessions were evaluated for stress responses. Four representatives were selected for further investigation (photosynthetic performance, biochemical markers, sugar content, specialized metabolites, transcription level of transcription factors NAC, HSF, DREB and expression of heat shock proteins HSP70 and HSP90): very sensitive (392), moderately sensitive (395), tolerant (404) and most tolerant (411). Accessions more tolerant to stress conditions were characterized by higher basal content of proline, total sugars, glucosinolates and higher transcription of NAC and DREB. Under all stress conditions, 392 was characterized by a significant decrease in biomass, root growth, photosynthesis performance, fructan content, especially under osmotic and combined stress, a significant increase in HSF transcription and HSP accumulation under temperature stress and a significant decrease in NAC transcription under all stresses. The most tolerant accession under all applied stresses, 411 showed the least changes in all analyzed parameters compared with the other accessions.