Amplification of an RNA template molecule was examined using the ligase ribozyme and its corresponding RNA substrates under alternating temperature conditions. Alternating temperatures enhanced the rate of the thermodynamically unfavorable dissociation of the annealed products into the two separate RNA templates, reminiscent of the polymerase chain reaction. Under these conditions, the RNA ligase ribozyme system was observed to amplify through a mainly cross‐catalytic process, generating additional copies of the starting RNA template molecules. Thus, template‐directed RNA ligation using the ribozyme under thermally fluctuating conditions will be an intriguing point to consider when explaining the primordial event of chemical evolution.