We constructed a new model to study the sensitivity of permafrost carbon stocks to future climate warming. The one-dimensional model solves an equation for diffusion of heat penetrating from the overlying atmosphere and takes into account additional in situ heat production by active soil microorganisms. Decomposition of frozen soil organic matter and produced CO2 and methane fluxes result from an interplay of soil heat conduction and phase transitions, respiration, methanogenesis and methanotrophy processes. Respiration and methanotrophy consume soil oxygen and thus can only develop in an aerated top-soil column. In contrast, methanogenesis is not limited by oxygen and can be sustained within the deep soil, releasing sufficient heat to further thaw in depth the frozen carbon-rich soil organic matter. Heat production that accompanies decomposition and methanotrophy can be an essential process providing positive feedback to atmospheric warming through self-sustaining transformation of initially frozen soil carbon into CO2 and CH4. This supplementary heat becomes crucial, however, only under certain climate conditions. Oxygen limitation to soil respiration slows down the process, so that the mean flux of carbon released during the phase of intense decomposition is more than two times less than without oxygen limitation. Taking into account methanogenesis increases the mean carbon flux by 20%. Part II of this study deals with mobilization of frozen carbon stock in transient climate change scenarios with more elaborated methane module, which makes it possible to consider more general cases with various site configurations. Part I (this manuscript) studies mobilization of 400 GtC carbon stock of the Yedoma in response to a stepwise rapid warming focusing on the role of supplementary heat that is released to the soil during decomposition of organic matter.