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• We experimentally study the axial heat-transfer in Taylor-Couette flow. • The axial heat-transfer and viscous-heating are decoupled using thermal waves. • The effects of boundary heat-loss on measured Nusselt number are modeled. • The measured Nusselt number is insensitive to oscillating period of thermal waves. • The correlations between axial Nusselt number and Taylor number, radius ratio are established. This study experimentally investigates the axial heat transfer of the secondary flow in the cylindrical annular gap around a flywheel within a canned reactor coolant pump, belonging to the Taylor-Couette (TC) flow. A dynamic method based on the transient temperature responses of the TC flow to the input thermal waves, where the axial heat transfer coefficient is determined by the amplitude decay and phase lag of axially propagating temperature waves, is proposed. The influences of viscous heating are distinguished using the mean temperature distribution, allowing for the performance of decoupling tests of axial heat transfer and viscous heating in TC flow. The modification of the boundary heat loss on the axial propagation of temperature waves in a rotor-fluid-stator TC system was modeled. The measured axial heat-transfer coefficient was insensitive to the oscillating periods of the input thermal waves within the maximum permitted period. The axial heat transfer coefficients with different Taylor numbers and radius ratios were measured based on the proposed method. The correlations between the axial heat-transfer coefficient and Taylor number satisfied the scaling law with an effective exponent of 0.5, but they change non-monotonically with respect to the radius ratio in highly turbulent TC flow. This study provides insight into the axial heat transfer characteristics of TC flow. [ABSTRACT FROM AUTHOR]