Context. Comets are small celestial bodies made of ice, dust, and rock that orbit the Sun. Understanding their behavior as they warm up at perihelion unveils many pieces of information about the interior and general morphology of the ices hidden under the dust. Aims. The goal of this research is to study the sublimation of CH4 through amorphous solid water (ASW), with a focus on the structural changes in water and the influence of a layer of indene (as a proxy of the crust) during a period of thermal processing, which we use in a controlled laboratory setting to simulate cometary environments. Methods. Ices at a CH4/H2O abundance ratio of about 0.01 are deposited and layered, or co-deposited, at 30 K and are heated until 200 K (or 140 K) with a ramp of either 1 or 5 K min-1. We use mass spectrometry and infrared spectroscopy to analyze the results. Results. Depending on the heating ramp and type of deposition, the sublimation of methane through ASW varies, being lower in intensity and higher in temperature when the co-deposited structure is considered. When two temperature cycles are applied, the second one sees less intense CH4 desorptions. When indene is placed above the ice mixtures, we find that the thicker its layer, the later the methane desorption. However, this later desorption sees a greater quantity of methane released due to water reorganization and higher desorbed material pressure. Conclusions. The structural changes of water ice drive volatile and hyper-volatile desorption because of the transition from high to low intrinsic density and transformation from amorphous to crystalline. This desorption indicates that such material has been deposited at low temperatures in agreement with previous theories on cometary ices formed in the pre-stellar cloud. During the two temperature cycles of our experiments, most of the released material is seen to be pristine and the processed part, if any, is of a negligible quantity, in agreement with dust-rock cometary studies.