Thermal engine for free piston compressor

The engine (1) has a turbomachine (2) i.e. gas turbine, comprising a compressor (20), a combustion chamber (23) and a turbine (26). A free piston compressor (3) is coupled with the turbomachine and comprises a compressor piston (30) and a cylinder chamber (31) with a cylinder and a motor piston (32). A part of a fluid i.e. air, conveyed through the compressor piston is supplied to the cylinder, and another part of the fluid is provided for tempering i.e. cooling, the combustion chamber and/or the turbine. An intercooler (50) is arranged between the compressor and the free piston compressor. Independent claims are also included for the following: (1) an aircraft engine (2) a method for operating a turbomachine (3) a method for increasing thrust of an aircraft engine.