The influence of climate on mosquito-borne diseases like dengue and chikungunya is well established, but comprehensively tracking long-term spatial and temporal trends across large areas has been hindered by fragmented data and limited analysis tools. This study presents an unprecedented analysis, in terms of breadth, estimating the susceptible-infectious-recovered transmission parameters from incidence data in all 5570 municipalities in Brazil over 14 years (2010-2023) for both dengue and chikungunya. We describe the Episcanner computational pipeline, developed to estimate these parameters, producing a reusable dataset characterizing all dengue and chikungunya epidemics that have taken place in this period in Brazil. The analysis reveals new insights into the climate-epidemic nexus: we identify distinct geographical and temporal patterns of arbovirus disease incidence across Brazil, highlighting how climatic factors like temperature and precipitation influence the timing and intensity of dengue and chikungunya epidemics. The innovative Episcanner tool empowers researchers and public health officials to explore these patterns in detail, facilitating targeted interventions and risk assessments. This research offers the possibility of exploring the main characteristics of dengue and chikungunya epidemics and their geographical specificities linked to the effects of global temperature fluctuations such as those captured by the El Niño-Southern Oscillation index.