Transcript levels powerfully influence cell behavior and phenotype and are carefully regulated at several steps. Recently developed single cell approaches such as RNA single molecule fluorescence in-situ hybridization (smFISH) have produced advances in our understanding of how these steps work within the cell. In comparison to single-cell sequencing, smFISH provides more accurate quantification of RNA levels. Additionally, transcript subcellular localization is directly visualized, enabling the analysis of transcription (initiation and elongation), RNA export and degradation. As part of our efforts to investigate how this type of analysis can generate improved models of gene expression, we used smFISH to quantify the kinetic expression of STL1 and CTT1 mRNAs in single Saccharomyces cerevisiae cells upon 0.2 and 0.4 M NaCl osmotic stress. In this Data Descriptor, we outline our procedure along with our data in the form of raw images and processed mRNA counts. We discuss how these data can be used to develop single cell modelling approaches, to study fundamental processes in transcription regulation and develop single cell image processing approaches.