In recent years there has been a growing interest in methane as an alternative rocket fuel due to its favourable specific gravity, storage temperature and thermal stability in addition to its ability to support In-Situ Resource Utilization. Due to these properties methane supports the ongoing design trend of strategic reduction in system complexity and increase of reusability. The current work presents a first step in addressing the lack of information in open literature on the characteristics of methane under conditions found in rocket nozzle cooling channels i.e. elevated inflow temperature and a high single sided heat load. A new experimental facility has been established at KTH - Royal Institute of Technology in cooperation with GKN Aerospace, and as part of ESA's Future Launcher Preparatory Programme. This facility is shown to enable direct measurement of the Heat Transfer Coefficient (HTC) of methane under a range of conditions, with a limited uncertainty and good repeatability. For inflow temperatures of around 400 K, mass flows up to 15 g/s and pressures up to 30 bar, it has been observed that the effect of single sided heating results in a significant development of the flow field, which influences the heat transfer in second half of the test section. This development results in an increase of the HTC towards the end of the cooling channel. No significant effect of the pressure on the HTC has been observed under the current experimental conditions.