Social media platforms shape climate action discourse. Mapping these online conversations is essential for effective communication strategies. TikTok's climate discussions are particularly relevant given its young, climate-concerned audience. In this work, we collect the first TikTok dataset on climate topics. We collected 590K videos from 14K creators along with their follower networks. By applying topic modeling to the video descriptions, we map the topics discussed on the platform on a climate taxonomy that we construct by consolidating existing categorizations. Results show TikTok creators primarily approach climate through the angle of lifestyle and dietary choices. By examining semantic connections between topics, we identified non-climate "gateway" topics that could draw new audiences into climate discussions.