Thermophoresis is the movement of molecules in a temperature gradient. For aqueous solutions its microscopic basis is debated. Understanding thermophoresis for this case is, however, important since it proved very useful to detect the binding affinity of biomolecules and since thermophoresis could have played an important role in early molecular evolution. Here we discuss why the thermophoresis of single- and double-stranded oligonucleotides - DNA and RNA - is surprisingly similar. This finding is understood by comparing the spherical capacitor model for single-stranded species with the case of a rod-shaped model for double-stranded oligonucleotides. The approach describes thermophoresis of DNA and RNA with fitted effective charges consistent with electrophoresis measurements and explains the similarity between single- and double-stranded species. We could not confirm the sign change for the thermophoresis of single- versus double-stranded DNA in crowded solutions containing polyethylene glycol [Y. T. Maeda, T. Tlusty, and A. Libchaber, Proc. Natl. Acad. Sci. USA 109, 17972 (2012)], but find a salt-independent offset while the Debye length dependence still satisfies the capacitor model. Overall, the analysis documents the continuous progress in the microscopic understanding of thermophoresis.