We theoretically consider two-dimensional moire transition metal dichalcogenide (TMD) bilayers, which are strongly correlated in the sense that the on-site Coulomb interaction is comparable to or larger than the hopping kinetic energy between the moire lattice sites. The system accommodates many symmetry-broken ground states both in charge and isospin sectors at various commensurate rational fillings such as 1/2, 1/3, 1/4, 2/3, etc. We investigate two complementary important aspects of the dependence of the symmetry breaking on (1) the range of the electron-electron interaction, which can in principle be experimentally controlled by the nearby gates and the dielectric environment, and (2) temperature, which could thermally suppress the symmetry breaking above a critical temperature. Experimental implications of the theory are discussed.