Heat storage apparatus comprising at least one thermal store (300) comprising a chamber (301) having a gas inlet (306), a gas outlet (307), and a gas-permeable thermal storage media (303) disposed therebetween, the apparatus being configured such that, during operation, the flow path of a gas flowing through the chamber (301) from inlet (306) to outlet (307) for transfer of thermal energy to or from the storage media (303) can be selectively altered in response to the progress of the thermal transfer, thereby enabling the flow path to bypass inactive upstream or downstream regions of the storage media where thermal transfer is complete or minimal, so as to minimize the pressure drop across the storage media. A baffle system (305) in a main flow passageway (312) may be used to control the gas flow path.