We report on experimental measurements of transient heat transfer characteristics of carbon nanotube (CNT) aggregates for the temperature range from 120K to 370K. Giant thermal transport relaxation time (τ) is observed: about 100s at room temperature and increased up to 260s at lower temperatures, one order of magnitude bigger than the biggest value reported so far in literatures. These unusual big τ values may imply significant thermal transport phase lag across CNT contacts. A relaxation time based model is proposed to characterize the transient thermal transport behavior between contacting CNTs. This finding may stimulate new ways to improve the efficiency of thermal energy conversion by using nanoscale materials.

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