Moderator temperature coefficient (MTC) and fuel Doppler temperature coefficient (DTC) are both the key reactivity coefficients for the safety assessment of a nuclear fission reactor core. Conventional unidirectional perturbing computation exhibits a limited scope in understanding the full-core physics. To better assist the energy policy decision making, this work contributes two different perturbation approaches to characterise the temperature coefficients of reactivity, i.e. by perturbing the moderator (or fuel) temperature while keeping the core power, or by perturbing the power while keeping the moderator (or fuel) temperature. Multi-physics computational codes suite (WIMS-PANTHER-Serpent) is employed to simulate and benchmark the startup core behavior of a nuclear new build currently occurring in the UK. Reasonably good agreements with the nuclear reactor physics are demonstrated computationally for both perturbation methods.