Molecular dynamics simulations have been widely used in exploring the nucleation behavior of many systems, including gas hydrates. Gas hydrates are ice-like solids in which gas molecules are trapped in water cages. During hydrate formation, a considerable amount of heat is released, and previous work has reported that the choice of temperature control scheme may affect the behavior of hydrate formation. The origins of this effect have remained an open question. To address this question, extensive NVE simulations and thermostatted (NPT and NVT) simulations with different temperature coupling strengths have been performed and compared for systems where a water nanodroplet is immersed in a H2S liquid. Detailed analysis of the hydrate structures and their mechanisms of formation has been carried out. Slower nucleation rates in NVE simulations in comparison to NPT simulations have been observed in agreement with previous studies. Probability distributions for various temperature measures along with their spatial distributions have been examined. Interestingly, a comparison of these temperature distributions reveals a small yet noticeable difference in the widths of the distributions for water. The somewhat reduced fluctuations in the temperature for the water species in the NVE simulations appear to be responsible for reducing the hydrate nucleation rate. We further conjecture that the NVE-impeded nucleation rate may be the result of the finite size of the surroundings (here the liquid H2S portion of the system). Additionally, a local spatial temperature gradient arising from the heat released during hydrate formation could not be detected.