NOVELTY - The engine system has an engine (10) with an exhaust gas heat exchanger (150) that is positioned along an exhaust system (73). A thermal energy storage device is in fluidic communication with the exhaust gas heat exchanger. An engine coolant heat exchanger is in thermal communication with the thermal energy storage device that includes a phase changing media which changes between liquid and solid phases. A bypass valve directs a working fluid from the thermal energy storage device through the engine coolant heat exchanger or around the engine coolant heat exchanger.    USE - Combustion engine system for hybrid vehicle.    ADVANTAGE - The energy is recovered from engine exhaust gases and the recovered energy is used to improve vehicle operation and to reduce fuel consumption of vehicle. The thermal energy is extracted and is provided to exhaust gas heat recovery system, so that engine starting and engine stopping time is improved. By extracting engine exhaust gas heat to a thermal energy storage device, it may be possible to provide the technical result of propelling a vehicle and maintaining a passenger cabin temperature while an engine has stopped rotating. The thermal energy storage device stores exhaust gas energy while the engine is combusting an air-fuel mixture, and thermal energy is released from the thermal energy storage device while the engine has stopped rotating while an electric machine is propelling the vehicle, so that heat is provided to the vehicle cabin without consuming electrical energy in electrical heater. The engine coolant pump is activated when heating the passenger cabin instead of operating an electric heater so that electrical power consumption is reduced.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is included for a method for operating an engine.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic block diagram of engine. (Drawing includes non-English language text)    Engine (10)    Fuel injector (66)    Exhaust system (73)    Exhaust gas heat exchanger (150)    Exhaust gas heat recovery system (151)