The spotted wing Drosophila, Drosophila suzukii, is a new pest in Europe and America which causes severe damages to stone fruits crops. Temperature and humidity are among the most important abiotic factors governing insect life. In many situations, temperature can become stressful thus compromising fitness and 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 submitted to six low (-5 to 7.5 °C) and seven high temperatures (30 to 37 °C) for various durations, and survival-time-temperature relationships were investigated. In addition, pupal thermal tolerance was analyzed under low vs. high relative humidity. Our results showed that males had higher cold survival than females, and pupae appeared less cold-tolerant than adults. Above 5 °C, adult cold mortality became minor, even after prolonged exposures (i.e. one month). Males were less heat tolerant than females, and pupae showed a better survival to extreme high temperatures than adults. Low relative humidity did not affect D. suzukii cold survival, but reduced survival under heat stress. Overall, this study shows that survival of D. suzukii under heat and cold conditions depends on both stress intensity and duration, and the methodological approach used here, which was based on thermal tolerance landscapes, provides a comprehensive description of D. suzukii thermal tolerance and limits.