In the present paper, an exact first-order statistical analysis is given of the power and temperature fluctuations in a nuclear power reactor with temperature feedback, which is perturbed by Gaussian white reactivity noise. Using a new technique, the time-independent Fokker-Planck equation for the two-dimensional power-temperature Markov process is solved in terms of a two-dimensional first-order characteristic function. This characteristic function gives a complete first-order statistical description of the investigated stochastic process and allows for the calculation of the marginal and the combined probability density functions of reactor power and temperature. In addition, a general expression for the moments is derived. Since the underlying reactor model has been extensively used in approximate linearized analyses, a comparison can be made of the exact results obtained in this paper with the earlier results, and the validity of the linear approximation can be delimited in terms of two dimensionless system parameters.