Under stress, cells orchestrate a complex regulatory response to maintain protein homeostasis, leveraging differential translational regulation for constitutively expressed mRNAs and the transcriptionally induced heat shock protein HSP70 transcripts. Constitutive mRNAs typically experience partial translational suppression, consistent with their partitioning into stress-induced phase-separated condensates and the global reduction in protein synthesis. In contrast, inducible HSP70 mRNAs bypass this repression to remain in the cytosol where they recruit the available components of the translational machinery to ensure the rapid synthesis of HSP70. Although the components involved in the preferential translation of HSP70 mRNA during heat stress have not been fully elucidated, differences in the mRNA and translation factors between yeast and mammals suggest organism-specific mechanisms of HSP70 mRNA translation. In this review, we consider these differences to discuss the current knowledge on heat shock regulation of translation. We extend the discussion to go beyond the cytosolic needs of HSP70 to ponder the important interplay between the cytosol and mitochondria in activating HSP70 accumulation, which becomes vital for preserving intercompartmental proteostasis and cell survival.