The spotted wing Drosophila, Drosophila suzukii, is a new pest in Europe and America which causes severe damages, mostly to stone fruit crops. Temperature and humidity are among the most important abiotic factors governing insect development and fitness. In many situations, temperature can become stressful thus compromising survival. The ability to cope with thermal stress depends on basal level of thermal tolerance. Basic knowledge on temperature-dependent mortality of D. suzukii is essential to facilitate management of this pest. The objective of the present study was to investigate D. suzukii basal cold and heat tolerance. Adults and pupae were subjected to six low temperatures (−5–7.5 °C) and seven high temperatures (30–37 °C) for various durations, and survival-time-temperature relationships were investigated. Data showed that males were globally more cold tolerant than females. At temperature above 5 °C, adult cold mortality became minor even after prolonged exposures (e.g., only 20% mortality after one month at 7.5 °C). Heat tolerance of males was lower than that of females at the highest tested temperatures (34, 35 and 37 °C). Pupae appeared much less cold tolerant than adults at all temperatures (e.g., Lt50 at 5° C: 4–5 d for adults vs. 21 h for pupae). Pupae were more heat tolerant than adults at the most extreme high temperatures (e.g., Lt50 at 37 °C: 30 min for adults vs. 4 h for pupae). The pupal thermal tolerance was further investigated under low vs. high humidity. Low relative humidity did not affect pupal cold survival, but it reduced survival under heat stress. Overall, this study shows that survival of D. suzukii under heat and cold conditions can vary with stress intensity, duration, humidity, sex and stage, and the methodological approach used here, which was based on thermal tolerance landscapes, provides a comprehensive description of D. suzukiithermal tolerance and limits.