Our research explores the impacts of climate change on Greece's cultural heritage, focusing on outdoor monuments, indoor museum environments, and economic implications. We examine how environmental changes contribute to the deterioration of ancient sites, affecting their preservation. In museums and historic buildings, fluctuations in temperature and humidity pose risks to artifact conservation. Additionally, we assess the economic impact of climate change on energy consumption for maintaining stable conditions in museums and cultural tourism. Our work highlights vulnerabilities and informs strategies for protecting cultural heritage in a changing climate.