A flexible sheet of aligned carbon nanotubes includes an array of aligned nanotubes held in a polymer matrix material. The carbon nanotubes have an average length of between about 50 microns and about 500 microns. The polymer matrix has an average thickness of between about 10 microns and about 500 microns. The flexible sheet has a density of about 0.2 to about 1.0 g/cc and includes between about 98 to about 60 weight percent aligned carbon nanotubes and between about 2 and about 40 weight percent polymer. A tape of aligned carbon nanotubes, a method for producing a tape of aligned carbon nanotubes, a method of producing the flexible aligned carbon nanotube sheet material and a method of increasing unidirectional heat conduction from a work piece are also disclosed.