There are always differences between the computer predicted temperatures of a spacecraft thermal model and the temperatures measured during the mandatory laboratory thermal tests. As a consequence, the model must be correlated before the spacecraft is launched to space, in order to identify the correct parameters that match the experimentally measured temperatures. A new technique is presented to identify the parameters, based on the minimization of the error of the transient equations which governs the heat transfer in the spacecraft. The steady state minimization was presented in a previous work, but the transient techniques presented hereafter enable a better and more extended identification of parameters despite the higher complexity of the computational problem. The use of a set of available subroutines (TOLMIN), which permits the constrained optimization of a general function, makes possible to ensure that the obtained parameters are non-negative, a requirement to have physical sense. The gradient function must be calculated for each problem, but this can be done automatically. Results show that for small and medium size transient Thermal Mathematical Models (TMM), a good correlation of thermal parameters can be achieved even if some of the nodes temperatures are not measured in the thermal tests.