Environmental Gene Regulatory Influence Networks (EGRINs) coordinate the timing and rate of gene expression in response to environmental and developmental signals. EGRINs encompass many layers of regulation, which culminate in changes in the level of accumulated transcripts. Here we infer EGRINs for the response of five tropical Asian rice cultivars to high temperatures, water deficit, and agricultural field conditions, by systematically integrating time series transcriptome data (720 RNA-seq libraries), patterns of nucleosome-free chromatin (18 ATAC-seq libraries), and the occurrence of known cis-regulatory elements. First, we identify 5,447 putative target genes for 445 transcription factors (TFs) by connecting TFs with genes with known cis-regulatory motifs in nucleosome-free chromatin regions proximal to transcriptional start sites (TSS) of genes. We then use network component analysis to estimate the regulatory activity for these TFs from the expression of these putative target genes. Finally, we inferred an EGRIN using the estimated TFA as the regulator. The EGRIN included regulatory interactions between 4,052 target genes regulated by 113 TFs. We resolved distinct regulatory roles for members of a large TF family, including a putative regulatory connection between abiotic stress and the circadian clock, as well as specific regulatory functions for TFs in the drought response. TFA estimation using network component analysis is an effective way of incorporating multiple genome-scale measurements into network inference and that supplementing data from controlled experimental conditions with data from outdoor field conditions increases the resolution for EGRIN inference.