This paper demonstrates an innovative data analysis for weather using Cloud Computing, integrating both system and application Data Science services to investigate extreme weather events. Identifying five existing projects with ongoing challenges, our aim is to process, analyze and visualize collected data, study implications and report meaningful findings. We demonstrate the use of Cloud Computing technologies, MapReduce and optimization techniques to simulate temperature distributions and analyze weather data. Two major cases are presented. The first case is focused on forecasting temperatures based on studying trends from the historical data of Sydney, Singapore and London to compare the historical and forecasted temperatures. The second case is to use five-step MapReduce for numerical data analysis and eight-step process for visualization, which is used to analyze and visualize temperature distributions in the United States, before, during and after the time of experiencing polar vortex, as well as in the United Kingdom during and after the flood. Optimization was used in experiments involved up to 100 nodes between Cloud and non-Cloud and compared performance with and without optimization. There was an improvement in performance between 20% and 30% under 60 nodes in Cloud. Results, discussion and comparison were presented. We justify our research contributions and explain thoroughly in the paper how the three goals can be met: (1) forecasting temperatures of three cities based on evaluating the trends from the historical data; (2) using five-step MapReduce to achieve shorter execution time on Cloud and (3) using eight-step MapReduce with optimization to achieve data visualization for temperature distributions on US and UK maps.