Heterostructures comprising silicon, molybdenum disulfide (MoS) and graphene are investigated with respect to the vertical current conduction mechanism. The measured current-voltage (I-V) characteristics exhibit temperature dependent asymmetric current, indicating thermally activated charge carrier transport. The data is compared and fitted to a current transport model that confirms thermionic emission as the responsible transport mechanism across the devices. Theoretical calculations in combination with the experimental data suggest that the heterojunction barrier from Si to MoS is linearly temperature dependent for T = 200 to 300 K with a positive temperature coefficient. The temperature dependence may be attributed to a change in band gap difference between Si and MoS, strain at the Si/MoS interface or different electron effective masses in Si and MoS, leading to a possible entropy change stemming from variation in density of states as electrons move from Si to MoS. The low barrier formed between Si and MoS and the resultant thermionic emission demonstrated here makes the present devices potential candidates as the emitter diode of graphene-base hot electron transistors for future high-speed electronics.