Thermal conductivity plays an important role in energy storage when the materials are charging and discharging. This paper presents an experimental investigation of the evolution of thermal conductivity up to 600 degrees C in different concretes. Moreover, the thermal conductivity was measured during thermal fatigue cycles when temperature ranged between 300 and 600 degrees C, simulating the operation conditions in a storage system of molten salts in a Concentrating Solar Power Plant (CSP). Five concrete compositions were analysed using diverse types of aggregates with different thermal response, covering a wide range of the initial thermal conductivity. The results confirm that the loss of thermal conductivity with temperature during the first heating is mainly due to the free water loss. Moreover, the type of aggregate influences the overall thermal performance of concrete due to its thermal conductivity and the volumetric differences with the cement paste. Siliceous aggregates underwent the highest decrease of thermal conductivity of concrete (+50%) with regard to room temperature. Regarding the cooling phase, thermal conductivity recovers between 20% and 40% depending on the type of aggregate. The outcomes of the present study demonstrate that the assumption of a constant thermal conductivity value in numerical simulations to predict its thermal capacity for energy storage is not appropriate.