This study contributes a first comparison of current and potential threats to Natural World Heritage Sites from climate change, as assessed by experts, when site and location characteristics (size, year of inscription to the World Heritage list, continent, climate zone and kind of site) are controlled for. The probability of a threat as well as its intensity is analysed. Another novelty lies in the use of data from the IUCN Conservation Outlook assessment, covering all 245 Natural and Mixed World Heritage Sites across the world for three points in time: 2014, 2017 and 2020. The threat of climate change is broadly defined and includes temperature extremes, rising temperatures, disappearing glaciers, coral bleaching, droughts, desertification, and rising sea levels. Results based on a simultaneous Probit model with random effects show that the probability of actual and potential climate change threats increases over time, but with differences for size, kind of site and location. The probability that a threat is identified is highest for marine and coastal sites, and for those in Latin America, while it is significantly lower for sites on the African continent. Larger sites have a higher probability of being assessed as at risk and the severity of threats is found to be lower for recently inscribed sites. The rate at which the likelihood of a threat assessment increases is consistent for both current and future situations, while the probability of the most severe threat is larger for the current than the future period. A serious threat from climate change is assessed as highest for locations in the tropical monsoon (current period) or the tropical savannah climate (future period). Estimations also show that pure descriptive statistics or bivariate correlations may not correctly identify the risk or the dignity of a threat.