Though high thermal conductivity polymer composites are prepared based on the thermal requirements, the effectiveness and overall heat transfer performance of the radiators have to be addressed comprehensively to validate the concerned efforts taken to prepare the high thermal conductivity polymer composites. In this article, theoretical analysis on the thermal performance of the cross flow type heat exchanger under convection is performed only by concentrating on the term thermal conductivity of the material. Micro channel based geometry is extracted from the given heat exchanger problem to reduce the complexities of simulation. The term cooling system performance index (CSPI) is used to achieve the expected targets in the present investigation. For shorter fins, the effect of thermal conductivity on the cooling system performance index under lower Reynolds number is insignificant. Further discussions on effect of thermal conductivity on various cases are presented with brief explanations.