A heat exchanger for transferring heat between two fluids consists of a shell surrounding at least two tube bundles attached at both ends to a tube header. Each of the tube bundles is constructed from a plurality of individual tubes that are twisted into identical helixes formed about a common helical axis. Because each individual tube is formed in the shape of a helix, rather than as a straight tube, thermal elongation of the individual tubes results in a considerably reduced axial force on the tube attachments and tube header. Use of multiple tube bundles wound with opposite twist direction improves spacing efficiency between tubes.