The solar cycle induces substantial changes in the solar wind, which can have an important effect on the structure of the global heliosphere. In the ecliptic the ram pressure can vary from one cycle to the other, being greater during periods of minimum activity. We investigate the response of the heliosphere to a temporally varying solar wind. Since neutral hydrogen is a key component in determining the large‐scale structure of the heliosphere, we employ a multifluid model in which the charge‐exchange interaction between neutral hydrogen and protons is included self‐consistently. The variability of the termination shock location is described and the response of the hydrogen wall to the temporal solar wind is discussed. Both two‐shock and one‐shock models are considered. The propagation of global shock waves analogous to those driven by global merged interactions (GMIR) is considered too for both one‐ and two‐shock models. The global response of the heliosphere to a single GMIR disturbance can last for nearly a solar cycle (∼9.5 years). As a result of both a variable solar cycle ram pressure and the presence of disturbances of global extent, such as GMIRs, the large‐scale heliosphere is most likely highly time‐dependent and dynamical.