Bar legend for a different function in mathematica

[djymndl07]

How Can I add bar Legend for g[t] in the following code in mathematica?
Thanks in advance?

f[t_] := t + 1
g[t_] := t^3 + 3*t + 12
ParametricPlot[{f[t]*Cos[\[Theta]], f[t]*Sin[\[Theta]]}, {t, 0, 1}, {\[Theta], 0, 2*Pi},
ColorFunction -> Function[{x, y, t}, ColorData["SolarColors"][Rescale[g[t], {g[0], g[1]}, {0, 1}]]]]

 

[DrClaude]

Add

PlotLegends -> BarLegend[{"SolarColors", {0, 1}}]

to the ParametricPlot.