Cells grow well only in a narrow range of physiological conditions. Surviving extreme conditions requires the instantaneous expression of chaperones that help to overcome stressful situations. To ensure the preferential synthesis of these heat-shock proteins, cells inhibit transcription, pre-mRNA processing and nuclear export of non-heat-shock transcripts, while stress-specific mRNAs are exclusively exported and translated. How cells manage the selective retention of regular transcripts and the simultaneous rapid export of heat-shock mRNAs is largely unknown. In Saccharomyces cerevisiae, the shuttling RNA adaptor proteins Npl3, Gbp2, Hrb1 and Nab2 are loaded co-transcriptionally onto growing pre-mRNAs. For nuclear export, they recruit the export-receptor heterodimer Mex67-Mtr2 (TAP-p15 in humans). Here we show that cellular stress induces the dissociation of Mex67 and its adaptor proteins from regular mRNAs to prevent general mRNA export. At the same time, heat-shock mRNAs are rapidly exported in association with Mex67, without the need for adapters. The immediate co-transcriptional loading of Mex67 onto heat-shock mRNAs involves Hsf1, a heat-shock transcription factor that binds to heat-shock-promoter elements in stress-responsive genes. An important difference between the export modes is that adaptor-protein-bound mRNAs undergo quality control, whereas stress-specific transcripts do not. In fact, regular mRNAs are converted into uncontrolled stress-responsive transcripts if expressed under the control of a heat-shock promoter, suggesting that whether an mRNA undergoes quality control is encrypted therein. Under normal conditions, Mex67 adaptor proteins are recruited for RNA surveillance, with only quality-controlled mRNAs allowed to associate with Mex67 and leave the nucleus. Thus, at the cost of error-free mRNA formation, heat-shock mRNAs are exported and translated without delay, allowing cells to survive extreme situations.