how to limit the temperature below the melting point and also how to deal with the singularity caused by fast deformation at high temperatures

Hello
I am dealing with a coupled problem of magnetic field and solid mechanic including plasticity deformation. As the copper is heated, the initial yield stress is reduced and also temperature increases.
Without considering phase change of copper at melting point, the temperature exceeds the melting point.
I was wondering how to limit the temperature below the melting point and also how to deal with the singularity caused by fast deformation at high temperatures?
I would be grateful for any help.
Sincerely
Behrooz