Background Recent epidemics of Zika virus (ZIKV) in the Pacific and the Americas have highlighted its potential as an emerging pathogen of global importance. Both Aedes (Ae . ) aegypti and Ae . albopictus are known to transmit ZIKV but variable vector competence has been observed between mosquito populations from different geographical regions and different virus strains. Since Australia remains at risk of ZIKV introduction, we evaluated the vector competence of local Ae . aegypti and Ae . albopictus for a Brazilian epidemic ZIKV strain. In addition, we evaluated the impact of daily temperature fluctuations around a mean of 28°C on ZIKV transmission and extrinsic incubation period. Methodology/Principal findings Mosquitoes were orally challenged with a Brazilian ZIKV strain (8.8 log CCID 50 /ml) and maintained at either 28°C constant or fluctuating temperature conditions. At 3, 7 and 14 days post-infection (dpi), ZIKV RNA copies were quantified in mosquito bodies, as well as wings and legs, using qRT-PCR, while virus antigen in saliva (a proxy for transmission) was detected using a cell culture ELISA. Despite high body and disseminated infection rates in both vectors, the transmission rates of ZIKV in saliva of Ae . aegypti (50–60%) were significantly higher than in Ae . albopictus (10%) at 14 dpi. Both species supported a high viral load in bodies, with no significant differences between constant and fluctuating temperature conditions. However, a significant difference in viral load in wings and legs between species was observed, with higher titres in Ae . aegypti maintained at constant temperature conditions. For ZIKV transmission to occur in Ae . aegypti , a disseminated virus load threshold of 7.59 log 10 copies had to be reached. Conclusions/Significance Australian Ae . aegypti are better able to transmit a Brazilian ZIKV strain than Ae . albopictus . The results are in agreement with the global consensus that Ae . aegypti is the major vector of ZIKV.