Mosquito-borne Zika virus (ZIKV) transmission has almost exclusively been detected in the tropics despite the distributions of its primary vectors extending farther into temperate regions. Therefore, it is unknown whether ZIKV's range has reached a temperature-dependent limit, or if it can spread into temperate climates. Using field-collected mosquitoes for biological relevance, we found that two common temperate mosquito species, Aedes albopictus and Ochlerotatus detritus, were competent for ZIKV. We orally exposed mosquitoes to ZIKV and held them at between 17 and 31°C, estimated the time required for mosquitoes to become infectious, and applied these data to a ZIKV spatial risk model. We identified a minimum temperature threshold for the transmission of ZIKV by mosquitoes between 17 and 19°C. Using these data, we generated standardized basic reproduction number R0-based risk maps and we derived estimates for the length of the transmission season for recent and future climate conditions. Our standardized R0-based risk maps show potential risk of ZIKV transmission beyond the current observed range in southern USA, southern China and southern European countries. Transmission risk is simulated to increase over southern and Eastern Europe, northern USA and temperate regions of Asia (northern China, southern Japan) in future climate scenarios.