Poor thermal transport within lithium-ion batteries fundamentally limits their performance, safety, and lifetime, in spite of external thermal management systems. All prior efforts to understand the origin of batteries' mysteriously high thermal resistance have been confined to ex situ measurements without understanding the impact of battery operation. Here, we develop a frequency-domain technique that employs sensors capable of measuring spatially resolved intrinsic thermal transport properties within a live battery while it is undergoing cycling. Our results reveal that the poor battery thermal transport is due to high thermal contact resistance between the separator and both electrode layers and worsens as a result of formation cycling, degrading total battery thermal transport by up to 70%. We develop a thermal model of these contact resistances to explain their origin. These contacts account for up to 65% of the total thermal resistance inside the battery, leading to far-reaching consequences for the thermal design of batteries. Our technique unlocks new thermal measurement capabilities for future battery research.