The residential heating sector accounts for a large share of the worldwide annual primary energy consumption. In order to reduce CO2-emissions, it is therefore particularly important to analyse this sector for potential efficiency improvements. In Europe, natural gas boilers are the most widely used heating technology since they are cost-effective and can be installed in any type of building. The energy efficiency of these boilers is already high. However, in their internal process, heat is generated at a high temperature level which is only used for space heating and therefore a high amount of exergy remains unused. This research aims to develop the potential of using the exergy to further improve the efficiency of the systems. A novel combination of methods is applied to analyse the thermodynamic behaviour of gas-fired boilers in detail and over the cycle of a year. The analysis is performed in two steps: In the first step a system is examined in stationary operating points. This is carried out through an experimental setup and a three-dimensional numerical simulation. In the second step, the obtained data is applied to a transient annual building simulation. The results show the temporal distribution and total amount of the annual exergy loss for a common residential building. The exergy loss accumulates to 16,271 kWh per year, which shows the high potential to partially convert the exergy to electrical energy and significantly reduce the external electricity demand and CO2-emissions of the building. Based on this, new technologies such as Thermoelectric Generators can be developed, which can enable this potential.