It is one of the efficient approach to reduce the memory consumption in Monte Carlo based reactor physical simulations by using the On-the-fly Doppler broadening for temperature dependent nuclear cross sections. RXSP is a nuclear cross sections processing code being developed by REAL team in Department of Engineering Physics in Tsinghua University, which has an excellent performance in Doppler broadening the temperature dependent continuous energy neutron cross sections. To meet the dual requirements of both accuracy and efficiency during the Monte Carlo simulations with many materials and many temperatures in it, this work enables the capability of on-the-fly pre-Doppler broadening cross sections during the neutron transport by coupling the Fast Doppler Broaden module in RXSP code embedded in the RMC code also being developed by REAL team in Tsinghua University. Additionally, the original OpenMP-based parallelism has been successfully converted into the MPI-based framework, being fully compatible with neutron transport in RMC code, which has achieved a vast parallel efficiency improvement. This work also provides a flexible approach to solve Monte Carlo based full core depletion calculation with many temperatures feedback in many isotopes.