As large language models (LLMs) are increasingly used, understanding their energy footprint has become an important concern. The growing adoption of retrieval-augmented (RAG) based pipelines for climate-domain specific analysis raises a key question: how does the energy consumption of domain-specific RAG-based pipelines compare with that of direct generic LLM usage? Prior research has focused on standalone model calls or coarse token-based estimates, while leaving the energy implications of deployed application workflows insufficiently understood. In this paper, we assess the inference-time energy consumption of two LLM-based climate analysis chatbots (ChatNetZero and ChatNDC) compared to the generic GPT-4o-mini model. We estimate energy use under actual user queries by decomposing each workflow into retrieval, generation, and hallucination-checking components. We also test across different times of day and geographic access locations. Our results show that the energy consumption of domain-specific RAG-based pipelines depends strongly on their design. More agentic pipelines substantially increase inference-time energy use, particularly when used for additional accuracy or verification checks, although they may not yield proportional gains in response quality. This study provides a new understanding on how the design of domain-specific LLM products affects both the energy footprint and quality of output.