Recent experimental studies [Z. Wu, B. Zhou, Z.B. Hu, Phys. Rev. Lett. 90 (2003) 048304] on an uncharged aqueous poly-N-isopropylacrylamide (PNIPAM) dispersion have shown that this microgel system is sensitive to temperature. This system was also experimentally found to be modeled quite well by microgel particles interacting via a hard-sphere repulsive plus an inverse power (temperature-dependent) attractive potential. To understand theoretically this thermally responsive PNIPAM dispersion, we apply a novel approach [G.F. Wang, S.K. Lai, Phys. Rev. E 70 (2004) 051402] to calculate its thermodynamic phase diagram. Differing from the conventional method in which the boundaries of the coexisting phases are the ultimate target, the present work places emphasis on crosshatching colloidal domains which include the homogeneous phase (gas, liquid or solid), two coexisting phases and perhaps also multi-phases in coexistence. Strategically, this was done by treating the coexisting phases as one composite system whose Helmholtz free energy density is written as the sum of constituent free energy densities each of which is weighed by its respective volume proportion. We show here that by minimizing the composite system's free energy density the phase-diagram domains can all be determined in addition to the phase boundaries customarily obtained by imposing the conditions of equal pressure and equal chemical potential. Also, we present the theoretically predicted phase diagram of PNIPAM dispersion and compare it with the one observed experimentally.