Temperature measurements of C$_2$ and CN radicals occurring in detonation waves through oxy-acetylene and oxy-cyanogen mixtures have been made by a brightness and emissivity method. In agreement with results obtained in their combustion systems, abnormally high temperatures are observed in the reaction zone. When the free expansion of the burnt gases is prevented by initiating the wave by the bursting of a diaphragm, the temperature drops to a final steady value in good agreement with thermodynamic calculations. The rate of fall of the temperature appears to be connected with the vibrational relaxation time of carbon monoxide (and of nitrogen in the case of cyanogen mixtures). It is possible that vibrationally excited carbon monoxide is formed in the reaction and this is responsible for the electronic excitation of the carbon radicals.