Malaria is endemic in South Sudan and it is one of the most severe diseases in the war-torn nation. There has been much concern about whether the severity of its transmission might depend upon climatic conditions that are related to the reproduction of the single-cell parasite attaching to female mosquitoes, especially in high altitude areas. The country experiences two different climatic conditions; namely one tropical and the other hot and semi-arid. In this study, we aim to assess the potential impact of climatic conditions on malaria prevalence in these two climatically distinct regions of South Sudan. We develop and analyze a host-mosquito disease-based model that includes temperature and rainfall. The model has also been parameterized in a Bayesian framework using Bayesian Markov Chain Monte Carlo (MCMC). The mathematical analysis for this study has included equilibria, stability and a sensitivity index on the basic reproduction number R0. The threshold R0 is also used to provide a numerical basis for further refinement and prediction of the impact of climate variability on malaria transmission intensity over the study region. The study highlights the impact of various temperature values on the population dynamics of the mosquito.