Oncogenes, such as c-Myc, enhance growth and proliferative signaling to promote continuous cell cycle divisions, the hallmark of cancer. The inadvertent consequence of this is an increase in cellular stresses. However, whether and how oncogenes can directly contribute to cellular stress tolerance, and how much cancer cells rely on these mechanisms for survival, remains poorly understood. Here we show that c-Mycdependent proteotoxic stress contributes to the generation of genotoxic stress. We reveal an important role for the transcription factor Heat Shock Factor 1 (HSF1) in the tolerance to both these c-Myc-induced stresses. c-Myc upregulates HSF1 directly, by activating its expression, and indirectly, via c-Mycdependent proteotoxic stress activation. In addition to relieving c-Myc-induced proteotoxic and genotoxic stress, HSF1 also enables DNA damage response signalling through γ H2AX. Consequently, acute depletion of HSF1 significantly increases c-Myc-driven genome instability and decreases cell viability. Our results establish that c-Myc-dependent regulation of HSF1 ensures that proteotoxic and genotoxic stress, resulting from c-Myc-induced enhanced growth and proliferation, are compatible with cell survival.