Due to their extremely high thermal conductivity, carbon nanotubes (CNTs) have received many research interests for thermal management applications. An advanced thermal interface structure made by two opposing, partially over-lapped CNT arrays is designed for thermally connecting two contact surfaces. The performance of this interface structure is thermally characterized using diffraction-limited infrared microscopy. Significant temperature discontinuities are found at the end of the CNT-CNT contact region, which indicates a large thermal resistance between CNTs. Due to this inter-tube resistance, the thermal performance of the CNT-based interface structure is far below expectation, with a thermal resistance value of about 3.8 × 10−4 K·m2/W. Possible mechanisms of heat transfer between CNTs, which result in the large inter-tube resistance, are discussed.