During the last decades, a vivid interest in the low heat rejection (LHR) diesel engine has arisen. In a LHR engine, an increased level of temperatures inside the cylinder is achieved resulting from the insulation applied to the combustion chamber walls. The steady-state LHR engine operation has been studied so far by applying either first- or second-law balances. However, very few works have treated this subject during the very important transient operation, with the results limited to the engine speed response. For this purpose, an experimentally validated simulation code of the thermodynamic cycle of the engine during transient conditions is applied. This takes into account the transient operation of the fuel pump, the development of friction torque using a detailed per degree crank angle sub-model, while the equations for each cylinder are solved individually and sequentially. In this work, two common insulators of various thicknesses are considered for the engine in hand, viz. silicon nitride and plasma spray zirconia. The transient response of various engine (e.g. speed, volumetric efficiency, fuel pump rack position, brake mean effective pressure and specific fuel consumption) and turbocharger variables is depicted and analyzed, with the results compared to the non-insulated transient and the insulated steady-state operation. For a more in-depth analysis of transient engine heat transfer, the interesting phenomenon of the short-term temperature (cyclic) oscillations in the combustion chamber walls during transients needs to be studied. To this aim, the thermodynamic model of the engine is appropriately coupled to a wall periodic heat conduction model, which uses the gas temperature variation as boundary condition throughout the engine cycle after being treated by Fourier analysis techniques. The evolution of many variables during the transient engine cycles, such as the amplitude of oscillation or gradient of temperature swing is thus illustrated. Moreover, the simulation code is expanded in a way to include the second-law balance, as this may prove an interesting alternative to the first-law analysis. It is revealed that after a ramp increase in load, the second-law values unlike the first-law ones are heavily impacted by the insulation scheme applied. Combustion and total engine irreversibilities decrease significantly (up to 24% for the cases examined) with increasing insulation. Unfortunately, this decrease is not transformed into an increase in piston work but rather increases the potential for extra work recovery owing to the higher availability content of the exhaust gas.