In the framework of Isothermal Compressed Air Energy Storage (CAES), a new finned piston compressor has been designed and realized at LEI laboratory in EPFL. This system comprises a series of concentric annuli’s fitting into each other compressing the air while keeping its temperature close to ambient thanks to increased heat transfer area. Modeling of heat transfer in such a complicated geometry with a transient, multi layer, multi dimensional nature can be best done by Thermo-Electric Analogy Method (TEAM). Using bond graph representation method and based on the previously developed model for a classic reciprocating compressor, energy conversion has been modeled based on equivalent electric circuits for both heat transfer and fluid flow bonds. Results have been verified using a test bench and to provide contrast to current technology, compared to a conventional reciprocating compressor.