How to colorize a rectangle with a given color function?

Question

I want to set color to a rectangle (in fact a line) that lies on (0,0) and (1,0), and the color function is given by $u(x,t)=t(x-x^2), 0\leq t\leq1$. Since, this $u(x,t)$ act as temperature at the point $(x,0)$ at time $t$, I want to use the colordata with "TemperatureMap", the following is what I have tried:

u[x_, t_] := t (x - x^2)
Animate[Plot[0, {x, 0, 1}, 
 AxesOrigin -> {0, 0}, 
 PlotRange -> {{0, 1}, {-0.02, 0.25}}, 
 PlotStyle -> {Thick}, 
 ColorFunction -> (ColorData["TemperatureMap"][u[#, t]]) &],
{t, 0, 1}]

I find that it must be some problem in the ColorFunction, but I can't fix it, any suggestion?

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I have tried your code, and find it shall works as the first answer, but since my original question (not posted here) is tried to solving the following question,

f[x_] := -x^2 + x
equ = {D[u[t, x], t] == D[u[t, x], x, x],
u[0, x] == f[x],
u[t, 0] == f[0],
u[t, 1] == f[1]};
sol = NDSolve[equ, u, {t, 0, 1}, {x, 0, 1}]
HeatConda = Animate[Show[{
Plot[Evaluate[u[t, x] /. sol], {x, 0, 1}, 
 PlotRange -> {-0.1, 0.25}, AxesOrigin -> {0, 0}, 
 Filling -> Axis, 
 ColorFunction -> (ColorData["TemperatureMap"][#2] &)],
Plot[-0.04, {x, 0, 1}, PlotStyle -> {Thick},
 ColorFunction ->
  Function[{x, y}, 
   ColorData["TemperatureMap"][Evaluate[u[t, x] /. sol]]]]}],
 {t, 0, 0.4}]

I want to color the bottom line as the same as the filling color. I first tried to simplify the question to the one post here, but the solution here still can work for my (original) question, so please help me again?

Answer 1

ColorFunction [] doesn't always perform proper scaling:

f[x_] := -x^2 + x
equ = {D[u[t, x], t] == D[u[t, x], x, x], u[0, x] == f[x],  u[t, 0] == f[0], u[t, 1] == f[1]};
sol = NDSolve[equ, u, {t, 0, 1}, {x, 0, 1}];
g[t_, x_] := Evaluate[u[t, x] /. sol][[1]];
{min, max} = {FindMinValue[{g[0, x], x > 0}, {x, 0}],
              FindMaxValue[{g[0, x], x > 0}, {x, 0}]}
HeatConda =
 Animate[Show[{
    Plot[g[t, x], {x, 0, 1},
     PlotRange -> {-0.1, 0.25},
     AxesOrigin -> {0, 0},
     Filling -> Axis,
     ColorFunction -> (ColorData["TemperatureMap"][#2] &)],
    Plot[-.05, {x, 0, 1}, 
     PlotStyle -> Thick,
     ColorFunction -> (ColorData["TemperatureMap"][Rescale[g[0., #1], {min, max}]] &)]
    }], {t, 0, 0.4}]