Combined high temperature and weak radiation stress negatively influences wheat production. However, related eco-physiological mechanisms across wheat species of different genetic backgrounds are not well documented. A pot-culture experiment was conducted in growth chambers to analyse the prevailing strategies of wheat genotypes with different ploidy levels under combined high temperature and weak radiation (30°C−25°C, 200 µmol m−2 s−1 photosynthetically active radiation (PAR)) stress compared with normal growth conditions (20°C−15°C; 400 µmol m−2 s−1 PAR). The diploid and tetraploid wheat genotypes showed better avoidance ability to high temperature and weak radiation stress than the hexaploids. These diploids and tetraploids produced high vegetative biomass under control conditions but this was reduced substantially under the stress. The adaptive response to avoid the stress was a strong reduction in vegetative organs, mainly leaf area. Consequently, these genotypes produced lower yields. By contrast, modern hexaploid wheat varieties displayed a stronger tolerance to the stress and produced higher yields through greater green leaf area, higher relative leaf water content, and higher proline and soluble sugar contents. The relative importance of these tolerance and avoidance strategies was estimated to account for 60% and 22%, respectively, of the variations in grain yield. Our study demonstrated that modern hexaploid wheat has acquired a greater proportion of tolerance rather than avoidance strategy in response to high temperature and weak radiation stress.