Amid accelerated digitalization, not only is the scale of data processing and storage increasing, but so too is the associated infrastructure load on the climate. Current climate models and environmental protocols almost entirely overlook the impact of information and communication technologies on the thermal and energy balance of the biosphere. This paper proposes the theory of information and climate feedback (ICF) as a new nonlinear model describing the loop of digitalization, energy consumption, the thermal footprint, the climatic response, and the vulnerability of digital infrastructure. The system is formalized via differential equations with delays and parameters of sensitivity, greenness, and phase stability. A multiscenario numerical analysis, phase reconstructions, and thermal cartography were conducted. Critical regimes, including digital overheating, fluctuational instability, and infrastructural collapse in the absence of adaptive measures, were identified. The paper concludes with the proposal of an international agreement titled the Green Digital Accord and a set of metrics for sustainable digitalization. This work integrates climatology, information technologies, and the political economy of sustainability.