The climate crisis is the most urgent challenge to life on Earth and is expected to worsen in the coming years. Among the UN’s Sustainable Development Goals (SDGs), Climate Action is crucial for addressing this crisis, with communication and climate education being key strategies. This study investigates the discourse of scientific outreach on social media, focusing on Instagram as a tool to meet SDG #13. Given that social media is the primary information source for Brazilians, profiles like Observatório do Clima (Climate Observatory) are significant in national climate discussions. Our study analyzed 46 Instagram posts from Climate Observatory, selected from the first month of each quarter in 2023. Using a Framing analysis, we categorized the posts into three areas: Climate Change, Emotions and Actions. Our results indicate that the climate change discourse was primarily framed as a scientific certainty, appearing in 30.56% of the posts. Identifying and describing the climate problem, which is essential for motivating action, was featured in 34.78% of the posts. The emotions conveyed included hope (30.43%) and fear (26.09%). Our findings indicate that the main goal of the Climate Observatory’s Instagram profile was to engage the public with scientific data, consistently reaffirming climate science. The use of emotions such as hope and fear played a crucial role in connecting with the audience and encouraging collective action. However, the rising issue of climate hopelessness and anxiety poses a challenge. Improving scientific communication about climate change is vital for enhancing understanding, seeking solutions, and promoting social well-being. Universities can apply framing methodology in their communication strategies to effectively reach their audiences, particularly for climate communication and achieving the Sustainable Development Goals.