NOVELTY - The method involves drawing fresh air through an interstitial space (142) of a double wall exhaust system to heat the air, and directing the heated air to an intake manifold (44) via a conduit (144) including a control valve during condition. The intake air is drawn from the intake manifold to and through the interstitial space via the conduit along opposite direction from the condition to cool exhaust gas during another condition different from the former condition. The former condition is given as engine combusting condition and non engine knocking condition.    USE - Method for providing Intake air heating and exhaust cooling in a multi-cylinder engine i.e. boosted petrol engine, of a propulsion system of an automobile by a double wall exhaust system i.e. exhaust-to-air heat exchanger.    ADVANTAGE - The method enables exhibit higher combustion and exhaust temperatures by a boosted engine than a naturally aspirated engine of similar output power, thus increasing nitrogen-oxide emissions from the engine by higher temperatures and accelerating materials ageing i.e. exhaust-after treatment catalyst ageing. The method enables providing exhaust-gas recirculation (EGR) by diluting intake air charge with exhaust gas, thus reducing oxygen content. The method enables using resulting air exhaust mixture in place of ordinary air to support combustion in the engine for producing lower combustion and exhaust temperatures result, thus improving fuel economy in petrol engines by reducing throttling losses and heat rejection. The method enables calculating desired intake air temperature to minimize pumping losses and engine warm-up time as a function of speed, load, ambient temperature, engine temperature and time since start. The method enables directing heated air into the intake manifold, thus enhancing fuel economy.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for a system for providing Intake air heating and exhaust cooling, comprising an exhaust system.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic block diagram of an engine.    Multi-cylinder engine (10)    Intake manifold (44)    Electronic driver (68)    Interstitial space (142)    Conduit (144)