The performance, safety, and reliability of electrochemical energy storage and conversion systems based on Li-ion cells depend critically on the nature of heat transfer in Li-ion cells, which occurs over multiple length scales, ranging from thin material layers all the way to large battery packs. Thermal phenomena in Li-ion cells are also closely coupled with other transport phenomena such as ionic and charge transport, making this a challenging, multidisciplinary problem. This review paper presents a critical analysis of recent research literature related to experimental measurement of multiscale thermal transport in Li-ion cells. Recent research on several topics related to thermal transport is summarized, including temperature and thermal property measurements, heat generation measurements, thermal management, and thermal runaway measurements on Li-ion materials, cells, and battery packs. Key measurement techniques and challenges in each of these fields are discussed. Critical directions for future research in these fields are identified.