As a cleaner, cheaper, and more globally evenly distributed fuel, natural gas has considerable environmental, economic, and political advantages over petroleum as a source of energy for the transportation sector. Despite these benefits, its low volumetric energy density at ambient temperature and pressure presents substantial challenges, particularly for light-duty vehicles with little space available for on-board fuel storage. Adsorbed natural gas systems have the potential to store high densities of methane (CH4, the principal component of natural gas) within a porous material at ambient temperature and moderate pressures. Although activated carbons, zeolites, and metal-organic frameworks have been investigated extensively for CH4 storage, there are practical challenges involved in designing systems with high capacities and in managing the thermal fluctuations associated with adsorbing and desorbing gas from the adsorbent. Here, we use a reversible phase transition in a metal-organic framework to maximize the deliverable capacity of CH4 while also providing internal heat management during adsorption and desorption. In particular, the flexible compounds Fe(bdp) and Co(bdp) (bdp(2-) = 1,4-benzenedipyrazolate) are shown to undergo a structural phase transition in response to specific CH4 pressures, resulting in adsorption and desorption isotherms that feature a sharp 'step'. Such behaviour enables greater storage capacities than have been achieved for classical adsorbents, while also reducing the amount of heat released during adsorption and the impact of cooling during desorption. The pressure and energy associated with the phase transition can be tuned either chemically or by application of mechanical pressure.