A process for determining a relative temperature distribution at a surface of a high temperature member to be used in a gas containing oxygen at high temperatures is disclosed. The process comprises the step of determining the relative surface temperature distribution of the member by measuring concentrations of oxygen at the surface of the member, which surface is composed of silicon carbide or silicon nitride. The process may also include the step of quantitatively determining a distribution of temperatures at the surface of the member by measuring concentrations of oxygen at the surface of the member, determining a relationship between temperatures and concentrations of oxygen on a surface of a standard member, and comparing the measured oxygen concentrations at the surface of the member with those of a standard member with reference to this relationship.