Chenopodium quinoa is a genetically diverse crop that can adapt to a wide range of environments, including temperatures and salinities. However, only a few studies have assessed the combined effects of two or more environmental factors on C. quinoa. Here, we investigated the effects of salinity (300 mM NaCl), elevated temperature (35 °C), and their interaction with growth, water–salt balance, the efficiency of photosystem II (PSII), the activity of cyclic electron transport (CET) around photosystem I (PSI), Rubisco and PEPC enzyme content, and the expression of photosynthetic genes. We found that elevated temperature did not decrease the biomass but caused a significant increase in the water and potassium content of C. quinoa leaves. The decrease in PSII efficiency under elevated temperature was accompanied by an increase in the expression of genes encoding the components of PSII (psbA) and linear electron transport (FDI), as well as the main photosynthetic protein Rubisco (rbcL). Moreover, the strongest effect was induced by the combined effect of elevated temperature and salinity, which induced high oxidative stress (a threefold increase in MDA), a threefold decrease in the biomass, a twofold decrease in PSII efficiency, and a two- to eightfold decrease in the expression of the photosynthetic genes psbA, FDI, and rbcL. PSI was more tolerant to all forms of stress; however, the combined effect of elevated temperature and salinity downregulated the expression of PGR5 and FNR1, which may diminish the role of PGR5/PGRL1-dependent CET in favor of the NDH-dependent CET of PSI. The obtained data on the functioning of photosystems and the expression of photosynthetic genes under combined stress (elevated temperature and salinity) can make a significant contribution to understanding the mechanisms of tolerance of C. quinoa to multiple stresses under climate change conditions.