•PA–SA/CNTs composite PCMs with different contents of CNTs (5–8wt.%) were prepared.•Thermal conductivities of PA–SA/CNTs were significantly improved due to the CNTs.•Thermal release rates of PA–SA/CNTs were much higher than that of PA–SA.•The prepared PA–SA/CNTs composite PCMs had a good thermal reliability. The effect of carbon nanotubes (CNTs) on thermal behavior of palmitic–stearic acid binary eutectic mixture (PA–SA) was investigated experimentally. Four samples of PA–SA/CNTs composite phase change materials (PCMs) with mass fractions of CNTs of 5–8wt.% at an increase of 1wt.% were prepared. The thermal properties of the PA–SA/CNTs composite PCMs characterized by Differential Scanning Calorimeter indicated that the phase change temperatures and latent heats of the composites changed slightly as the change of the mass fraction of CNTs. The thermal conductivities of the PA–SA/CNTs composite PCMs increased by 20.2%, 26.2%, 26.2% and 29.7% respectively when the mass fractions of CNTs were 5wt.%, 6wt.%, 7wt.% and 8wt.%. The thermal performance test results showed that the thermal release rate of the prepared composite PCMs increased due to the addition of CNTs while the storage rate decreased. Thermal cycling test results revealed that the PA–SA/CNTs composite PCMs performed well in thermal reliability.