We developed a method to produce time-varying maps for dengue transmission risk, using the Ross-Macdonald framework and differential equations to estimate spatially the basic reproduction number (R0) of a vector-borne disease. The components of the R0 formula were derived partly from a mosquito population dynamics model integrating meteorological and environmental variables, and partly from temperature-dependent functions of vector competence and the extrinsic incubation period. The method was applied on Reunion Island, a tropical island located in the Indian Ocean, where the mosquito Aedes (Stegomyia) albopictus has been responsible for large and numerous outbreaks of dengue. As a validation, predicted maps and dynamic outputs were compared with the distribution of confirmed dengue cases registered during the year 2018 in Reunion Island. The results highlight strong agreements between the observed epidemiological patterns and predicted R0 distribution and temporal dynamics. This finding demonstrates the relevance and efficiency of the spatialised basic reproduction number (R0) to develop an operational dynamic mapping tool for dengue surveillance and control. The resulting method could be of great use in a health policy-making context, providing a time and space awareness to the dengue risk perception.