Abstract: A second-order material temperature perturbation algorithm applicable to the full-energy range of non-thermalized isotopes based on the RMC code was developed, and a corresponding method for solving temperature derivatives of cross-section was proposed. The perturbation algorithm is based on the differential operator method, which is well-established in Monte Carlo codes and already implemented in RMC. Therefore, it is not reiterated in this paper, with the primary focus placed on establishing the temperature derivative of cross-section calculation model required by the method. The energy-region division for neutron cross-section processing in RMC was introduced firstly, followed by separate investigations into the online cross-section treatment methods and the temperature derivative of cross-section calculation methods for different energy regions. In the low-energy region, a cross-section adjustment factor was used for online processing, and based on this factor, a method for calculating the temperature derivative of cross-section was derived, with further investigation into its approximate calculation methods. In the resolved resonance region, a cross-section broadening technique based on Gauss-Hermite quadrature and the corresponding temperature derivative solution method were presented. In the unresolved resonance region, an equal-probability-band probability table generation method, along with an online cross-section processing approach and a temperature derivative solution based on this probability table, was proposed. Subsequently, the application of the equal-probability-band probability table and the calculation of temperature derivatives of cross-section were implemented using an innovative structure HDF5 format neutron nuclear databases. The correctness of the equal-probability-band probability table generation method was verified by comparing the k_eff and neutron spectrum calculation results of the Big Ten benchmark using conventional probability tables and equal-probability-band probability tables. Finally, the proposed algorithm was applied to calculate fuel temperature sensitivity coefficients for the Big Ten benchmark model, VERA-2B benchmark model, and VENUS-2 reactor benchmark model. Using the fuel temperature sensitivity coefficients obtained at a specific temperature, response counts at other temperature points were predicted. The results show that, in the vicinity of the current temperature, the deviation between the predicted and actual calculated results does not exceed three times the Monte Carlo statistical error, demonstrating the correctness of the algorithm and its applicability to large-scale complex problems.