Crank-rocker engine (CRE) is an internal combustion (IC) engine with a curved piston and cylinder, developed at Universiti Teknologi PETRONAS (UTP) Malaysia. Heat is generated during combustion in an IC engine, some portion of which is converted into the mechanical energy. Almost 30 of the generated heat needs to be dissipated through engine walls. Fins are used to provide additional surface area to engine block for dissipation of excess heat. Transient thermal analysis of existing 3-fins model of CRE is performed at different engine speeds, using 'ANSYS Transient Thermal' module. With the understanding of thermal behavior of the existing 3-fins model, new straight and curved conformal fin models, with increased surface area and better fin effectiveness, are proposed. Thermal performance of both, straight and curved fin models, is compared with existing 3-fins model of crank-rocker engine. © 2019 PENERBIT AKADEMIA BARU.