The present invention relates to a method and to an apparatus for improving the efficiency of a heat generator destined to heat a feed fluid such as water. The method according to the invention provides for the performance of a first heat exchange between at least a first flow rate of feed fluid and a flow rate of combustion air so as to heat the combustion air and cool the first flow rate of fluid from a first to a second temperature. The method also provides for the performance of a second heat exchange between the feed fluid at said second temperature and at least part of the flue gases produced by the heat generator so as to cool said flue gases and heat the feed fluid from said second to a third temperature. The method also provides for regulation of the flow rate of flue gases subjected to the second heat exchange as a function of the temperature reached by the fluid following the same second heat exchange.