We have investigated the dynamics of the phase transition between swollen isotropic and shrunken nematic states for a nematic network swollen in nematic solvent. The kinetics of swelling and shrinking driven by temperature (T)-jumps across the nematic-isotropic (N-I) transition temperature (T-NI(G)) strongly depends on the distance of destination temperature (T-d) from T-NI(G) (DeltaT). When Td is far above T-NI(G), the N --> I transition completes fast within the T-jump, which yields the swelling process of totally isotropic gel without coupling of N --> I transition. If T-d is moderately above TNIG, the N - I transition slowly proceeds from surface toward center of gel with accompanying swelling. In this case, the total swelling process is composed of two different stages, i.e., during N --> I transition and after N --> I transition: The former is a thermally activated process strongly coupled with N --> I transition; the latter is the T-independent swelling process of totally isotropic gel. When the T-quench from isotropic phase to nematic phase is sufficiently deep, the I --> N transition and shrinking proceed uniformly whereas the process is decelerated with increasing the degree of total volume change. In the case of Td slightly above (or below) T-NI(G), the onset of the N --> I (or I --> N transtion) is governed by heterogeneous nucleation, and the following growth of the nuclei yields considerably nonuniform swelling (or shrinking). The resulting dynamics becomes markedly slower than that observed after the T-jumps with sufficiently large DeltaT.