A heating system for a vehicle includes a reaction space (16) containing a first reactant (22) and a reactant storage space (20) containing or/and receiving a second reactant (24), wherein the first reactant and the second reactant form such a reaction system. A reaction of the first reactant with the second reactant produces a reaction product that releases heat. The second reactant can be separated from the first reactant by introducing heat into the reaction product. A reactant-releasing device (26) releases second reactant from the reactant storage space into the reaction space (16). A first heat removal device (58) removes heat from the first reactant or/and reaction product contained in the reaction space (16). A heating unit (52) heats the first reactant or/and heats the reaction product contained in the reaction space. A reactant-recirculating device (36) recirculates second reactant from the reaction space into the reactant storage space.