Galaxy clusters are known as the largest and most massive gravitationally bound objects in the Universe. X-ray observations discovered a large amount of diffuse, hot X-ray emitting gas with temperature of 10^7-8 Kelvin (so-called intracluster medium; ICM) trapped in deep gravitational potential well of galaxy cluster for the first time. Since the total mass of the ICM is estimated as ~ 10^14 solar mass and is a factor of ~5 larger than the integrated total mass of member galaxies in a galaxy cluster, the ICM plays an important role in the thermal evolution of baryons. Cool cores are often found at the center of galaxy clusters. They are in the form of the dense, relatively cool, metal enriched ICM. The presence of cool cores poses a challenge for our understanding of the thermal evolution of the baryons. In this talk, I will firstly introduce this challenge recognized as a long-standing problem in cluster astrophysics. Next, I will present our recent study that is possible to solve this problem. In addition, I will introduce a new generation X-ray observatory XRISM that will open a new window to X-ray astronomy.