Vertically aligned arrays of carbon nanotubes (CNTs) are attractive for a wide range of macroscopic applications which can exploit the remarkable properties of individual nanotubes. In this work, an abnormal behavior of CNT bundles in heat conduction is discovered under the transient electro-thermal characterization. The measured voltage change over the sample shows a dual-pace thermal response (DTR), which could not be fitted using a single thermal diffusivity heat transfer model. Instead, two thermal diffusivities are determined from the DTR phenomenon. Three rounds of cryogenic experiments are conducted to investigate the physics behind DTR phenomenon. It starts to emerge when the temperature is reduced to a certain level. After two rounds of cryogenic experiments, the DTR phenomenon becomes permanent from 295 K to 10 K. The nano-scale structure separation induced by the increased thermal strain leads to macroscale structure separation, which results in two parallel heat conduction paths responsible for the DTR phenomenon. By building a new parallel heat transfer model taking both the transient and steady-state electrical and thermal response into consideration, the area ratio of separated CNTs is determined. This result uncovers the existence of coiled morphology and nano-structure evolution of CNTs under cryogenic state and its effect on thermal and electrical transport, especially on their transient behaviors. Knowledge of the thermal transport in these CNTs arrays is important considering the fact that transient thermal response strongly affects their mechanical, optical, and electrical behaviors.