This study aims to establish a new thermal comfort index for evaluating air-conditioning systems, and introduces a new thermal comfort index for the provided and required temperatures. The authors performed comparison verification experiments on the temperature distribution of radiant air-conditioning and convective air-conditioning systems. The results showed the temperature provided by the convective air-conditioning system to have a wide distribution, unlike that of the radiant air-conditioning system. Based on these results, the authors propose a probabilistic thermal acceptability evaluation using the concepts of "provided temperature" and "required temperature". The authors consider this evaluation method to be applicable for non-steady thermal environments as well as uniform high quality indoor thermal environments using radiant air-conditioning systems, and personalized air-conditioning systems.