Apparatus and method for performing a nucleic acid amplification reaction and preferably a polymerase chain reaction (PCR) in a reaction mixture in at least one capillary tube. Several different embodiments are disclosed. One embodiment cycles a sample through a capillary tube loop passing through two thermostatted fluid baths. Another embodiment has the capillary tube routed alternatingly between two heat exchangers to that the sample makes only one pass through the tube. Other embodiments maintain the heat exchangers stationary and translate the samples between them. Still further embodiments maintain the samples stationary and either automatically translate or rotate the heat exchangers past the samples contained within the capillary tubes to perform the thermal cycles necessary for the amplification reaction.