The model LPJmL, which is a dynamic global vegetation model could help you to estimate the effect of climate change on rice. This model belongs to PIK, Potsdam, Germany. You should contact the necessary people and collaborate to make simulations.
I would suggest using a generic low fidelity differential equation method (like Christopher Teh). Once you integrate it with a dynamic climate change model, you can use more explicit crop models.
Decision Support System for Agrotechnology Transfer (DSSAT) has a rice module that can also be of assistance to your research. Evaluate, the options and choose a model based on your research question