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Superfluid helium-4 (He II) has been widely utilized as a coolant in various scientific and engineering applications due to its superior heat transfer capability. An important parameter required in the design of many He II based cooling systems is the peak heat flux $q^*$, which refers to the threshold heat flux above which boiling spontaneously occurs in He II. Past experimental and numerical studies showed that $q^*$ increases when the heating time $t_h$ is reduced, which leads to an intuitive expectation that very high $q^*$ may be achievable at sufficiently small $t_h$. Knowledge on how $q^*$ actually behaves at small $t_h$ is important for applications such as laser ablation in He II. Here we present a numerical study on the evolution of the thermodynamic state of the He II in front of a planar heater by solving the He II two-fluid equations of motion. For an applied heat flux, we determine the heating time beyond which the He II near the heater transits to the vapor phase. As such, a curve correlating $q^*$ and $t_h$ can be obtained, which nicely reproduces some relevant experimental data. Surprisingly, we find that there exists a critical peak heat flux $q^*_c$, above which boiling occurs nearly instantaneously regardless of $t_h$. We reveal that the boiling in this regime is essentially cavitation caused by the combined effects of the first-sound and the second-sound waves in He II. Based on this physical picture, an analytical model for $q^*_c$ is developed, which reproduces the simulated $q^*_c$ values at various He II bath temperatures and hydrostatic head pressures. This work represents a major progress in our understanding of transient heat transfer in He II., Comment: 8 pages, 7 figures