Two-nucleon momentum correlation functions are investigated for different single thermal sources at given initial temperature (T ) and density (ρ). To this end, the space-time evolutions of various single excited nuclei at T = 1 − 20 M eV and ρ = 0.2 -1.2 ρ0 are simulated by using the thermal isospin-dependent quantum molecular dynamics (T hIQM D) model. Momentum correlation functions of identical proton-pairs (Cpp(q)) or neutron-pairs (Cnn(q)) at small relative momenta are calculated by Lednick ý and Lyuboshitz analytical method. The results illustrate that Cpp(q) and Cnn(q) are sensitive to the source size (A) at lower T or higher ρ, but almost not at higher T or lower ρ. And the sensitivities become stronger for smaller source. Moreover, the T , ρ and A dependencies of the Gaussian source radii are also extracted by fitting the two-proton momentum correlation functions, and the results are consistent with the above conclusions.