The earliest cells may have consisted of a self-replicating genetic polymer encapsulated within a self-replicating membrane vesicle. Here, we show that vesicles composed of simple single-chain amphiphiles such as fatty acids, fatty alcohols, and fatty-acid glycerol esters are extremely thermostable and retain internal RNA and DNA oligonucleotides at temperatures ranging from 0 degrees C to 100 degrees C. The strands of encapsulated double-stranded DNA can be separated by denaturation at high temperature while being retained within vesicles, implying that strand separation in primitive protocells could have been mediated by thermal fluctuations without the loss of genetic material from the protocell. At elevated temperatures, complex charged molecules such as nucleotides cross fatty-acid-based membranes very rapidly, suggesting that high temperature excursions may have facilitated nutrient uptake before the evolution of advanced membrane transporters. The thermostability of these membranes is consistent with the spontaneous replication of encapsulated nucleic acids by the alternation of template-copying chemistry at low temperature with strand-separation and nutrient uptake at high temperature.