Studies of gene expression quantitative trait loci (eQTL) in different organisms have shown the existence of eQTL hot spots: each being a small segment of DNA sequence that harbors the eQTL of a large number of genes. Two questions of great interest about eQTL hot spots arise: (1) which gene within the hot spot is responsible for the linkages, i.e. which gene is the quantitative trait gene (QTG)? (2) How does a QTG affect the expression levels of many genes linked to it? Answers to the first question can be offered by available biological evidence or by statistical methods. The second question is harder to address. One simple situation is that the QTG encodes a transcription factor (TF), which regulates the expression of genes linked to it. However, previous results have shown that TFs are not overrepresented in the eQTL hot spots. In this article, we consider the scenario that the propagation of genetic perturbation from a QTG to other linked genes is mediated by the TF activity. We develop a procedure to detect the eQTL modules (eQTL hot spots together with linked genes) that are compatible with this scenario.