In this paper, a reduced morphological transformation model with spatially dependent composition and elastic modulus is considered. The parareal in time algorithm introduced by Lions et al. is developed for longer-time simulation. The fine solver is based on a second-order scheme in reciprocal space, and the coarse solver is based on a multi-model backward Euler scheme, which is fast and less expensive. Numerical simulations concerning the composition with a random noise and a discontinuous curve are performed. Some microstructure characteristics at very low temperature are obtained by a variable temperature technique.