Evolving systems rely on the storage and replication of genetic information. Here we present an autonomous, purely thermally driven replication mechanism. A pool of hairpin molecules, derived from transfer RNA replicates the succession of a two-letter code. Energy is first stored thermally in metastable hairpins. Thereafter, energy is released by a highly specific and exponential replication with a duplication time of 30 s, which is much faster than the tendency to produce false positives in the absence of template. Our experiments propose a physical rather than a chemical scenario for the autonomous replication of protein encoding information in a disequilibrium setting.