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Thermal properties of the diamond nanothread (DNT) forest array are studied using non-equilibrium molecular dynamics simulations. We find a strong anisotropic thermal property in this structure, i.e. the thermal conductivity in thread direction is over 300 times of that in the perpendicular direction. When subject to external strain, the thermal conductivity of the DNT forest decreases with increasing compressive/tensile strain in the thread direction, while thermal conductivity increases exponentially with increasing compressive strain in the perpendicular direction. The increase in thermal conductivity is attributed to the enhanced interactions among DNTs induced by compression. These results are explained by phonon spectra and structural deformation. Our findings show that diamond nanothread forest has a great potential application in the super-capacitors. [ABSTRACT FROM AUTHOR]