Abstract: The miniaturization of electronic devices and the fluctuation of power have made the problem of local overheating more prominent. The traditional constant thermal boundary conditions are unable to reflect the transient responses of the temperature on the heat surface and the interface heat transfer. This study develops a numerical model of conjugate natural convection in a square cavity filled with an Ag-MgO/water hybrid nanofluid and subjected to a periodic heat flux. The effects of the solid-to-fluid thermal-conductivity ratio ( R_k ), dimensionless frequency ( f ), total particle volume fraction ( \phi ), and heat-flux Rayleigh number ( Ra_q ) on the wall temperature drop, fluid-side interfacial heat transfer, local temperature response, and periodic energy transmission are examined. At Ra_q = 10^7 , f = 0.25 , and \phi = 0 , increasing R_k from 0.1 to 10 reduces the mean temperature of the outer heated surface at the peak heat-flux phase from 2.119 to 0.127. The fraction of the total temperature drop across the solid wall decreases from 95.16% to 17.13%, whereas the corresponding fraction across the fluid domain increases from 4.84% to 82.87%. Over the same range, Nu_T decreases by only about 2.2%, showing that R_k mainly redistributes the temperature drop between the solid wall and the fluid domain. At Ra_q = 10^7 , Nu_T increases by approximately 3.8% at \phi = 1\text% and by about 4.4% at \phi = 2\text% , with both values evaluated relative to the base fluid. These gains are similar for the three values of R_k , and the along-interface profile of the local Nu retains essentially the same shape. For fixed R_k and \phi , changing f from 0.1 to 1 alters Nu_T by no more than 0.015%. However, for the representative case with R_k = 10 and \phi = 2\text% , the peak-to-peak temperature variation at the solid monitoring point decreases from 2.878 × 10⁻³ to 1.280 × 10⁻⁴, while the temperature variation at the fluid monitoring point is also strongly attenuated. The frequency therefore affects the amplitude and phase propagation of the local temperature response much more strongly than the period-averaged interfacial heat transfer. For R_k = 0.1 , f = 1 , and \phi = 0 , an input heat-flux half-amplitude of 50% produces a half-amplitude of about 0.57% in the outer heated-surface temperature and about 0.011% in the solid-domain mean temperature; the heat-flux fluctuations transmitted to the conjugate interface and the cold wall decrease further to the order of 10⁻⁴%. Finally, at R_k = 1 and f = 0.25 , Nu_T increases as Ra_q rises from 10⁶ to 10⁸, with power-law exponents of 0.2229 ~ 0.2246 and local exponents of 0.2167 ~ 0.2316. The enhancement associated with particle loading increases slowly with Ra_q . These results show that R_k primarily governs temperature-drop allocation, \phi modifies the period-averaged interfacial heat-transfer level, f controls the transient thermal response, and Ra_q governs the overall increase in heat transfer.