The physical temperature of shock is an important parameter for weapon ammunition performance testing and the characterization of material states in extreme environments. Accurate acquisition of temperature has vital significance in the fields of national defence and industrial manufacturing. The shock process has characteristics of short duration, difficulty in contact-based measurements, and a wide temperature range, which can cause the failure of conventional temperature measurement methods. This paper proposes a temperature measurement method based on multi-spectral radiometry, which obtain the values of material radiation intensity. The inversion model based on Plancks radiation law can obtain the shock physical temperature value. In practice, the randomness of different target emissivity can cause large errors using the temperature inversion model. The emissivity model of the material during the shock process is more difficult to obtain. Meanwhile, the materials structure under shock may change in phase, which leads to a change in the emissivity model. Therefore, it is difficult to accurately obtain the shock physical temperature value by directly assuming the emissivity model. In this paper, the temperature calculation in multi-spectral temperature measurement experiments turned into a constrained optimization problem based on the constrained optimization theory. The temperature value obtained for each channel should be the same, limiting the object emissivity to a specific range. The constraint optimization algorithm calculates the target temperature and emissivity, which can overcome unknown emissivity for a shock physical temperature solution. At the same time, the combination of Equilibrium Optimizer and Sequential Quadratic Programming is applied to the solution of the temperature model, which avoids the shortcomings of poor stability and slow speed of a single algorithm. It improves the efficiency and accuracy of temperature inversion. The emissivity data of four common emissivity models at 3 000 K are simulated and verified. The results show that the temperature inversion error is less than 1%, and an inversion time is within 3 seconds. Finally, the temperature inversion of copper under shock compression is carried out using this algorithm. Compared with the Least Squares Method and Interior Point Penalty Function Method, the results indicate that the method proposed in this paper obtains the impact physical temperature value of copper more closely to the theoretical calculation. Therefore, this method provides an effective inversion approach for obtaining the physical temperature of other targets with unknown emissivity models.