The ability to respond evolutionarily to increasing temperatures is important for survival of ectotherms in a changing climate. Recent studies suggest that upper thermal limits may be evolutionary constrained. We address this hypothesis in a laboratory evolution experiment, encompassing ecologically relevant thermal regimes. To examine the potential for species to respond to climate change, we exposed replicate populations of Drosophila melanogaster to increasing temperatures (0.3 °C every generation) for 20 generations, whereas corresponding replicate control populations were held at benign thermal conditions throughout the experiment. We hypothesized that replicate populations exposed to increasing temperatures would show increased resistance to warm and dry environments compared with replicate control populations. Contrasting replicate populations held at the two thermal regimes showed (i) an increase in desiccation resistance and a decline in heat knock‐down resistance in replicate populations exposed to increasing temperatures, (ii) similar egg‐to‐adult viability and fecundity in replicate populations from the two thermal regimes, when assessed at high stressful temperatures and (iii) no difference in nucleotide diversity between thermal regimes. The limited scope for adaptive evolutionary responses shown in this study highlights the challenges faced by ectotherms under climate change.