Thermal measurements of heat capacity and thermal conductivity in a wide range of insulators and superconductors exhibit a “thermal paradox”: a large linear specific heat reminiscent of neutral Fermi surfaces (associated with fractionalized quasiparticles) in nonmetallic samples that exhibit no corresponding linear temperature coefficient to the thermal conductivity. At first sight, these observations appear to support the formation of a continuum of thermally localized many-body excitations, a form of many-body localization that would be fascinating in its own right. Here, by mapping thermal conductivity measurements onto thermal $RC$ circuits, we argue that the development of extremely long thermal relaxation times, a “thermal bottleneck,” is likely in systems with either many-body localization or neutral Fermi surfaces due to the large ratio between the electron and phonon specific heat capacities. We present a reevaluation of thermal conductivity measurements in materials exhibiting a thermal paradox that can be used in future experiments to deliberate between these two exciting alternatives.

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• Heat transfer
• Thermal conductivity
• Strongly correlated systems