In the 21st century, global climate change is a key concern for countries all over the world as, in the future, crops will face several extreme events, including an increase of 2–4 °C in the mean temperature with a possible consequent reduction in yield. Wheat (Triticum durum Desf) is one of the most important foods as it provides 20% of the protein for the world population. Since temperature is one of the most limiting factors of crop development, the aim of this trial was to verify the agronomic response of durum wheat to a temperature increase of about 1.5–2.0 °C through the use of short-time adjustment techniques, such as sowing time and variety choice. The experiment foresaw the comparison between two different temperature conditions (ordinary, OT—in the open field, and high, HT—under a polyethylene tunnel), two sowing times (ordinary—OS, and delayed—DS), and three varieties (Ofanto, modern variety; Cappelli, traditional variety; and a mix of the two). HT conditions caused a decline in the wheat yield (−52.5%), but without differences between the two sowing times. The grain quality resulted positively when affected by late sowing times with an increase in 1000 seeds weight and protein percentages and a decrease in shrunken grains. Therefore, it seems that in areas characterized by high temperatures, delayed sowing can improve grain quality without reducing yield quantity compared to ordinary sowing times.