1) Start with Google or PubMed with target gene name and other key words.
2) What cells/tissues you have used in finding the differential expression is another good info. You could infer the genes are the cell lineage or tissue-specific genes. Find the cell-specific other genes are studied with what TFs.
3) The status of cells studied whether you treated or infected or other abnormal condition is another good clue to narrow down your search.
4) Find other cell types showing upregulation of the gene list.
5) Start experimenting with general components of transcriptional complex by over-expressing TFs. There will be binding affinity or binding or association with unknown TFs.
Presently, there are a number of databases those have the TF information along with there binding sites. But only data is not enough to find the regulators (TFs). We have done the similar in-silico analyses in our previous research (PLoS ONE 10(9):e0137295, 2015 ; Frontiers in Plant Science 7, 2016, DOI: 10.3389/fpls.2016.01303).
There are different computational strategies to find out (based on prediction) the putative set of TFs regulating specific genes. Here we should keep in our mind that 'Regulation' of any gene depends on Tissue/cell type (spatial), time point (temporal) and condition (the 'Treated samples' in which you got the differential expression). Things become more complex when you consider that the TFs are more likely to act as combinations rather than singly. We have already addressed this issue in our PLoS ONE publication. I can help you in a better way if you can elaborate the details of your experiments/data and purpose of finding.
you can probably start to annotate your DEG list(s) with Homer or GREAT. It will give you an idea of specific pathways which are enriched among your DEG, together with (hopefully) some enrichment in TF binding sites in their promoters. You can also (if you work on a common species) look for your DEG genomic coordinates, and mine through different databases (I would suggest ENCODE) to see if any specific TF as binding sites close to you genes and make enrichment calculations (using Binomial or hypergeometric tests, for example). You may also use the MEME suite tools to predict potential TF binding sites, provided that you know the sequence of you genes promoters / regulatory sequences. Good luck!