ABSTRACT As artificial intelligence transitions from tool-based interaction toward ambient, environment-level integration, questions of sustainability, human capacity, and long-term alignment become structural rather than ethical preferences. This paper introduces a minimal set of thermodynamic operators governing warmth stability in ambient AI environments. These operators do not prescribe behaviour, ideology, or optimisation goals. Instead, they formalise constraints under which warmth, care, and alignment remain viable across time and scale. The operator set consists of four mechanisms: reversible stress (ΔR), explicit recovery (ΔR⁺), hysteresis of warmth thresholds (W₀ drift), and warmth sustainability (Λ₋). Together, they describe when stress remains reversible, when recovery increases future capacity, how historical pressure alters system sensitivity, and when locally warm behaviour becomes globally extractive. The operators are architecture-agnostic and apply equally to human systems, care environments, and AI-mediated ambient infrastructures. They are intended as a reference layer for ambient AI design, ensuring that intelligent environments remain inhabitable, non-extractive, and thermodynamically stable as they scale.