Adsorption thermal storage and transformation (ATST) of low-temperature heat is an energy saving technology towards the efficient use of renewable and waste heat. A solid sorption thermal battery (SSTB) is a promising concept for low-grade heat storage, combined cooling and heating, integrated energy storage and energy upgrade. Current progress in SSTB is related to the selection of advanced adsorbents and cycles which are properly adapted to ATST in various climatic zones. This paper mainly addresses such adaptation for China, Russia, and India which are among the top CO2 emitters and partially for Italy and Portugal. First, climatic data for selected cities of these countries were analyzed to specify adsorbents optimal from the thermodynamic point of view. It was found that an innovative sorbent “LiCl inside Multi-Wall Carbon NanoTubes (MWCNT)” is one of the most promising and universal for SSTB operating in several selected climatic conditions. To further elucidate the composite usability, especially, in cooling/(air conditioning) cycles, the experimental dynamic study of methanol sorption on this sorbent was performed. The study included shaping the LiCl/MWCNT composite as grains using polyvinyl alcohol as a binder, and the measurements of methanol sorption/desorption dynamics under conditions of the selected ATST cycle. The dynamics, studied by a Large Temperature Jump method, revealed the fast ad/desorption that led to high specific power and smaller SSTBs. Hence, the selected composite is a promising candidate for SSTB applications in the climatic zones involved.