[en] We develop a computationally tractable method for calculating correlation functions of the finite temperature trapped Bose gas that includes the effects of s-wave interactions. Our approach uses a classical field method to model the low energy modes and treats the high energy modes using a Hartree-Fock description. We present results of first and second order correlation functions, in position and momentum space, for an experimentally realistic system in the temperature range of 0.6T_c to 1.0T_c. We also characterize the spatial coherence length of the system. Our theory should be applicable in the critical region where experiments are now able to measure first and second order correlations