In this paper, the current state of the art on a new adsorptive cycle (the so-called “Heat from Cold” or HeCol), recently suggested for upgrading the ambient heat (Aristov, 2017), is surveyed. The survey includes theoretical and experimental parts. In the first one, the cycle efficiency and an optimal adsorbent are discussed. Requirements to the adsorbent optimal for this cycle from thermodynamic and kinetic points of view are formulated in terms of the Dubinin–Polanyi adsorption potential. The experimental part includes the dynamic study of the adsorbent regeneration stage and testing of a first lab-scale HeCol prototype to prove the feasibility of the HeCol concept. Advanced composite sorbents of methanol on the base of inorganic salts confined to porous matrices are synthesized and studied, including their testing in the first HeCol prototype. Finally, future development of the HeCol concept is discussed.