I fully recommend the CRISSP model which allows simulating dynamic processes of river ice including thermal effect. You can find 2dimensional version of the software CRISSP2D or 1 dimensional CRISSP1D.
Please note is not hydrologic model - is hydraulic model, allowing simulate unsteady flow conditions.
As far as I know the software is available from CEATI, Canada however I don’t know the price for the software.