One of the main issues that has limited the use of hydrogen as an energy vector for a long time is its low energy density per unit of volume. Alternative chemical storage methods have been developed in recent years to overcome the limitations associated with compressed or liquified hydrogen storage. One of these is the Liquid Organic Hydrogen Carrier (LOHC), which utilizes organic hydrocarbons that can capture hydrogen (through an exothermic hydrogenation reaction) and release hydrogen (through an endothermic dehydrogenation reaction). In this paper, a 0D model of an internal combustion engine fueled with a mixture of hydrogen and methane was used to investigate whether the enthalpy of the exhaust gases can balance the heat rate required to self-sustain the dehydrogenation stage. Two LOHC+ compounds were considered, namely, Perhydro-dibenzyltoluene and Perhydro-N-Ethylcarbazole. Four different hydrogen-to-methane ratios were considered, assuming an engine maximum brake power ranging from 500 to 6000 RPM. An energy balance was performed, balancing the dehydrogenation heat rate and the exhaust gas cooling heat rate, in order to establish the minimum temperatures of the exhaust gases required to self-sustain the LOHC+ dehydrogenation. We demonstrated that the minimum exhaust temperatures required to self-sustain the process in different running regimes and at different hydrogen-to-methane ratios are lower than literature and experimental exhaust temperatures.