Language models are increasingly expected to support users in stressful or uncertain situations, where warmth and empathy are desirable. While recent work links warmer models to lower factuality and reliability, we show that this conclusion is incomplete: prior studies often use warmth as a global persona and conflate tone effects with SFT data distribution shift. We revisit this issue through prompting, fine-tuning, factual robustness, and empathy evaluation, using an 11-dataset benchmark suite and EmoFact, a benchmark for factual accuracy under emotional context. Across three large language models, we find that warmth effects are task- and model-dependent, and that task-aligned adaptive tone can improve empathy while preserving reliability. We further train human-validated empathy evaluators to evaluate the output of our finetuned model. Our results suggest that models can be made more supportive in human relationships and social interactions without compromising overall reliability.