The early stage of formation of gas hydrates has recently attracted attention as amorphous intermediate gas hydrate structures have been observed, apparently contrary to a classical model of nucleation and some experimental observations. To date, essentially all reported molecular simulations of the nucleation of gas hydrates have been under constant temperature conditions, which does not consider the possible impacts of heat transfer on the nucleation processes. Here we show, using constant energy molecular simulations, that the nuclei at an early stage of the hydrate formation have relatively more crystalline order in comparison with those observed in previous isothermal (NPT or NVT) work. The current work suggests a more transient role for intermediate amorphous structures during hydrate nucleation, thereby providing a stronger link between molecular simulation and experimental observations. Our NVE results nevertheless support the two-step nucleation mechanism proposed in previous simulation studies under constant temperature conditions which features the initial formation of amorphous hydrate-like structures.