Single cell RNA sequencing can yield high-resolution cell-type-specific expression signatures that reveal new cell types and the developmental trajectories of cell lineages. Here, we apply this approach to Arabidopsis (Arabidopsis thaliana) root cells to capture gene expression in 3,121 root cells. We analyze these data with Monocle 3, which orders single cell transcriptomes in an unsupervised manner and uses machine learning to reconstruct single cell developmental trajectories along pseudotime. We identify hundreds of genes with cell-type-specific expression, with pseudotime analysis of several cell lineages revealing both known and novel genes that are expressed along a developmental trajectory. We identify transcription factor motifs that are enriched in early and late cells, together with the corresponding candidate transcription factors that likely drive the observed expression patterns. We assess and interpret changes in total RNA expression along developmental trajectories and show that trajectory branch points mark developmental decisions. Finally, by applying heat stress to whole seedlings, we address the longstanding question of possible heterogeneity among cell types in the response to an abiotic stress. Although the response of canonical heat-shock genes dominates expression across cell types, subtle but significant differences in other genes can be detected among cell types. Taken together, our results demonstrate that single cell transcriptomics holds promise for studying plant development and plant physiology with unprecedented resolution.