A sheet structure comprising: a plurality of linear structure bundles (12a-12c) each of which comprises a plurality of linear structures of carbon atoms, the linear structures within each bundle being arranged so as to be spaced from each other at a first gap and the respective bundles being arranged so as to be spaced from each other at a second gap which is larger than the first gap, the plurality of linear structure bundles (12a, 12b) comprising those of a first group of bundles, each of which bundles is tapered with one end thereof on the same side of the structure as a first surface being smaller than the other end thereof on the same side of the structure as a second surface, and those of a second group of bundles, each of which bundles is tapered with one end thereof on the same side of the structure as the first surface being larger than the other end thereof on the same side of the structure as the second surface; a filling layer filling the second gap and supporting the plurality of linear structure bundles (12a-12c); characterized in that a first coating film is formed over the first surface so as to be in contact with respective one ends of the plurality of linear structure bundles (12a-12c) and having a higher thermal conductivity than the filling layer; and a second coating film is formed over the second surface so as to be in contact with respective other ends of the plurality of linear structure bundles (12a-12c) and having a higher thermal conductivity than the filling layer; a third coating film is formed on surfaces of the linear structure bundles of the first group and having a higher thermal conductivity than the filling layer; and a fourth coating film is formed on surfaces of the linear structure bundles of the second group and having a higher thermal conductivity than the filling layer. a plurality of linear structure bundles (12a-12c) each of which comprises a plurality of linear structures of carbon atoms, the linear structures within each bundle being arranged so as to be spaced from each other at a first gap and the respective bundles being arranged so as to be spaced from each other at a second gap which is larger than the first gap, the plurality of linear structure bundles (12a, 12b) comprising those of a first group of bundles, each of which bundles is tapered with one end thereof on the same side of the structure as a first surface being smaller than the other end thereof on the same side of the structure as a second surface, and those of a second group of bundles, each of which bundles is tapered with one end thereof on the same side of the structure as the first surface being larger than the other end thereof on the same side of the structure as the second surface; a filling layer filling the second gap and supporting the plurality of linear structure bundles (12a-12c); characterized in that a first coating film is formed over the first surface so as to be in contact with respective one ends of the plurality of linear structure bundles (12a-12c) and having a higher thermal conductivity than the filling layer; and a second coating film is formed over the second surface so as to be in contact with respective other ends of the plurality of linear structure bundles (12a-12c) and having a higher thermal conductivity than the filling layer; a third coating film is formed on surfaces of the linear structure bundles of the first group and having a higher thermal conductivity than the filling layer; and a fourth coating film is formed on surfaces of the linear structure bundles of the second group and having a higher thermal conductivity than the filling layer.