A deterministic SEIR model of rift valley fever (RVF) with climate change parameters was considered to compute the basic reproduction number R-0 and investigate the impact of temperature and precipitation on R-0. To study the effect of model parameters to R-0, sensitivity and elasticity analysis of R-0 were performed. When temperature and precipitation effects are not considered, R-0 is more sensitive to the expected number of infected Aedes spp. due to one infected livestock and more elastic to the expected number of infected livestock due to one infected Aedes spp. When climatic data are used, R-0 is found to be more sensitive and elastic to the expected number of infected eggs laid by Aedes spp. via transovarial transmission, followed by the expected number of infected livestock due to one infected Aedes spp. and the expected number of infected Aedes spp. due to one infected livestock for both regions Arusha and Dodoma. These results call for attention to parameters regarding incubation period, the adequate contact rate of Aedes spp. and livestock, the infective periods of livestock and Aedes spp., and the vertical transmission in Aedes species.