There is this method proposed by kelvin, which is an alternative to direct heating. In this method, the fuel instead of direct heating is first fed to a heat engine and the work obtained is used to operate a heat pump operating between the ambient and the room to be heated. The sink of the heat engine is the room, the result being that the heat dumped per unit fuel burned is greater than the heat obtained by direct heating. Is there a particular name to this method/device. I need this topic for my seminar.
What you describe is simply called a heat pump. In your case it is driven by a heat engine instead of an electric motor. Refrigeration units that work on this principle and which are driven by small gasoline or diesel engines are very commonly used to keep truck trailers carrying perishables cold during road transit.
The economics of a heat engine-driven heat pump are determined by the availability of sufficient heat in the ambient (the "cold sink") to justify using the heat pump mechanism to extract it. For electrically-driven heat pumps, once the ambient temperature falls below a critical value, the heat pump furnishes insufficient gain and you are better off using the electricity instead to "directly" heat the space. It should be possible to determine that critical temperature for a gas engine-powered heat pump as well but I have not seen the derivation.