A thermodynamic analysis was carried out for a new “Heat from Cold” (HeCol) adsorption cycle for transformation of the ambient heat using the following working pairs: activated carbon ASM-35.4–methanol or composite sorbent LiCl/silica gel–methanol. Unlike the conventional cycle of an adsorption thermal engine where the adsorbent is regenerated at a constant pressure by its heating up to 80–150°C, the adsorbent in the HeCol cycle is regenerated by depressurization, which is performed due to a low ambient temperature. The balances of energy and entropy are calculated at each cycle stage and each element of the transformer under conditions of ideal heat transfer. The performance of the cycle for both pairs is compared. The threshold ambient temperature above which useful heat is not produced has been determined. The threshold values depend only on the absorption potential of methanol. It is demonstrated that useful heat with a high temperature potential of approximately 40°C can be obtained from a natural source of low-potential heat (such as a river, lake, or sea) only at a sufficiently low ambient temperature. The cycle with the composite sorbent LiCl/silica gel–methanol yielded much more useful heat than the cycle with the activated carbon ASM-35.4–methanol due to the features of the characteristic curve for methanol vapor adsorption on the composite sorbent. The amount of useful heat increases with decreasing ambient temperature and increasing temperature of the natural low-temperature heat source. The examined cycle can be used for upgrading the ambient heat temperature potential in countries with a cold climate.