The present invention provides a method and apparatus for amplifying a nucleic acid sequence by polymerase chain reaction (PCR). The method comprises placing a PCR sample in a container which is heated by only a single heat source that provides a high temperature for denaturation in the bottom of the PCR sample, while annealing and extension automatically occur in different regions of the PCR sample due to the convection induced by a temperature gradient descending from the bottom of the PCR sample to the surface of the PCR sample.