I will describe the universal aspect of unitary conformal field theories in the high-temperature limit with a global symmetry group G, where G can be a discrete group or a compact Lie group. I will describe the geometric setup to apply the spurion analysis and explain how we can capture this universal aspect up to a constant factor that depends on the choice of a theory. We consider as examples free field CFTs and holographic CFTs of the RN black holes with and without hair. We find that the RNAdS black hole with non-abelian hair is thermodynamically more stable than the one without hair.