A dry-cooling system useful in absorbing heat from a heat source and related dry cooling methods including a depolymerization cooling unit (DCU) in fluid communication with a polymerization heating unit (PHU). The DCU includes a DCU heat exchanger which receives a polymer and a catalyst, wherein contact of the polymer and the catalyst within the DCU heat exchanger causes an endothermic reaction, converting the polymer to a monomer and drawing heat from a first heat source. The monomer is then withdrawn from the DCU. The PHU includes a PHU heat exchanger, which receives the monomer, wherein contact of the monomer with the catalyst causes an exothermic reaction within the PHU heat exchanger, converting the monomer to the polymer. The polymer is then withdrawn from the PHU for conveyance back to the DCU, and the cycle is repeated.