Climate change is threatening human health in unprecedented orders and many ways. These threats are expected to grow unless effective and evidence-based policies are developed and acted upon to minimize or eliminate them. Attaining such a task requires the highest degree of the flow of knowledge from science into policy. The multidisciplinary, location-specific, and vastness of published science makes it challenging to keep track of novel work in this area, as well as making the traditional knowledge synthesis methods inefficient in infusing science into policy. To this end, we consider developing multiple domain-specific language models (LMs) with different variations from Climate- and Health-related information, which can serve as a foundational step toward capturing available knowledge to enable solving different tasks, such as detecting similarities between climate- and health-related concepts, fact-checking, relation extraction, evidence of health effects to policy text generation, and more. To our knowledge, this is the first work that proposes developing multiple domain-specific language models for the considered domains. We will make the developed models, resources, and codebase available for the researchers.