We investigate a volcanic hydrothermal system by using numerical simulation with three key observables as reference: the magnetic total field, vent temperature, and heat flux. We model the shallow hydrothermal system of Mt. Tokachidake, central Hokkaido, Japan, as a case study. At this volcano, continuous demagnetization has been observed since at least 2008, suggesting heat accumulation beneath the active crater area. The surficial thermal manifestation has been waning since 2000. We perform numerical simulations of heat and mass flow within a modeled edifice at various conditions and calculate associated magnetic total field changes due to the thermomagnetic effect. We focus on the system's response for up to a decade after permeability is reduced at a certain depth in the modeled conduit. Our numerical simulations reveal that (1) conduit obstruction (i.e., permeability reduction in the conduit) tends to bring about a decrease in vent temperature and heat flux, as well as heat accumulation below the level of the obstruction, (2) the recorded changes cannot be consistently explained by changing heat supply from depth, and (3) caprock structure plays a key role in controlling the location of heating and pressurization. Although conduit obstruction may be caused by either physical or chemical processes in general, the latter seems more likely in the case of Mt. Tokachidake.