Adsorptive transformation of heat is an emerging technology that is especially promising for low-temperature heat sources. Recently, an adsorption cycle (the so-called “Heat from Cold” or HeCol) has been suggested for upgrading the ambient heat in cold countries. This paper addresses the selection of composite sorbents of methanol specialized for this cycle and the study of their sorption properties. First, we analyzed which adsorbent is optimal for the HeCol cycle and how its properties depend on the HeCol cycle boundary temperatures. Then, three composite sorbents, based on CaCl2, CaBr2 and their mixture confined inside the silica gel mesopores, were prepared and their sorption equilibrium with methanol was analyzed keeping in mind the HeCol cycles with various boundary temperatures. It was shown, that these composite sorbents exchange up to 0.48 g of methanol per 1 g of the composite that far exceeds this value for common activated carbons. Finally, a first lab-scale HeCol prototype was built and tested with one of the studied sorbents, namely CaClBr/SiO2, to evaluate the feasibility of the cycle.