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Plotting the Johnson-Cook strength model

I'm trying to plot the stress-strain curve described by the Johnson-Cook strength (and eventually damage) models. The strength model is defined as:

σ=[A+Bεn][1+C ln(ε_dot*)][1-T*m]

where A, B, C, n, and m are material constants, ε_dot* is the non-dimensionalized strain rate, and T* is the homologous temperature where T*=(T-T0)/(Tmelt-T0)

To calculate the thermal softening (term in the last bracket of the J-C model), I need to determine the increase in temperature related to an increase in stress (and strain). I'm using the following equation:

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