The ability of a material to conduct heat influences many physical phenomena, ranging from thermal management in nanoscale devices to thermoelectrics. Van der Waals 2D materials offer a versatile platform to tailor heat transfer due to their high surface-to-volume ratio and mechanical flexibility. Here, the nanoscale thermal properties of 2D indium selenide (InSe) are studied by scanning thermal microscopy. The high electrical conductivity, broad-band optical absorption, and mechanical flexibility of 2D InSe are accompanied by an anomalous low thermal conductivity (κ). This can be smaller than that of low-κ dielectrics, such as silicon oxide, and it decreases with reducing the lateral size and/or thickness of InSe. The thermal response is probed in free-standing InSe layers as well as layers supported by a substrate, revealing the role of interfacial thermal resistance, phonon scattering, and strain. These thermal properties are critical for future emerging technologies, such as field-effect transistors that require efficient heat dissipation or thermoelectric energy conversion with low-κ, high electron mobility 2D materials, such as InSe.