The focus of the present investigation is on the development of an efficient estimation strategy of the temperature dependent capacitance and conductance matrices of the heat conduction problem expressed in a projection reduced order model. This problem arises in particular in the context of hypersonic vehicles where reduced order and surrogate modeling methods are particularly desirable to dramatically reduce the computational effort. The approach presented here recognizes that the structure undergoes a temperature rise which is not uniform but exhibits only relatively small variations around a uniform distribution. This expected property is used in a Taylor series format to permit a direct evaluation of the temperature dependent capacitance and conductance matrices which does not require the rebuilding of the thermal full finite element model. The accuracy of the proposed approach is evaluated, and found excellent, on a well-known baseline problem.