The Onset of Nucleate Boiling (ONB) marks the start of boiling heat transfer in a system designed for boiling heat transfer. ONB is dependent on the way the heat is generated within the heater. In applications such as nuclear reactors, during reactivity-initiated accidents, the heat generation is exponential, and hence an excursion in the heater temperature is observed. Similarly, in applications such as immersion cooling of microelectronics, the heat generated within the chip is a function of the load it is subjected to. In such cases, the point of ONB can shift and lead to an increase in the chip temperature. To avoid such an event and effectively design the chip cooling system, the knowledge of the change in the superheat at ONB with the heating rate is essential. In this work, ONB conditions are predicted by a model based on transient conduction and Hsu’s nucleation criterion. Numerical solutions are obtained for exponentially increasing heat flux. Different heating rates and bulk temperatures are explored. It is found that ONB heat flux and wall superheat increase with an increase in heating rate, whereas the total heat added till ONB decreases with an increase in heating rate. Subcooling increases the ONB wall superheat, ONB heat flux, and total heat added till ONB.