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First of all, I tried to directly use the 'heatMap' function in my answermy answer. I just tried it with the data in that post:

First of all, I tried to directly use the 'heatMap' function in my answer. I just tried it with the data in that post:

First of all, I tried to directly use the 'heatMap' function in my answer. I just tried it with the data in that post:

4 Added one-dimensional heat line (PDF plot)
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Edit 3

I also see the question asks for a "heatline" - if I understand this as a line plot, one could get it very straightforwardly:

Plot[Evaluate@PDF[SmoothKernelDistribution[data, .02], x], {x, 0, 1}]

heatline

This is simply a plot of the one-dimensional probability density function for the data set, smoothed with bandwidth .02.

Edit 3

I also see the question asks for a "heatline" - if I understand this as a line plot, one could get it very straightforwardly:

Plot[Evaluate@PDF[SmoothKernelDistribution[data, .02], x], {x, 0, 1}]

heatline

This is simply a plot of the one-dimensional probability density function for the data set, smoothed with bandwidth .02.

3 Simpler method for purely one-dimensional lists
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Edit 2

Of course, we can also backtrack even further and go to the original data set you started with - which was purely one-dimensional. In that situation, you can simply do something like this:

data = RandomReal[1, 100];

DensityPlot[
 Evaluate[{PDF[SmoothKernelDistribution[data, .02], x], 0}], {x, 0, 
  1}, {y, 0, .04}, AspectRatio -> Automatic, PlotPoints -> {200, 2}, 
 FrameTicks -> {Automatic, None}, PlotRangePadding -> None]

No Smearing

This involves no need for smearing in the vertical direction because it calculates the density function one-dimensionally in the first place. The methods above have their justification too, when the data list does have two-dimensional points that you want to project onto a single axis.

Edit 2

Of course, we can also backtrack even further and go to the original data set you started with - which was purely one-dimensional. In that situation, you can simply do something like this:

data = RandomReal[1, 100];

DensityPlot[
 Evaluate[{PDF[SmoothKernelDistribution[data, .02], x], 0}], {x, 0, 
  1}, {y, 0, .04}, AspectRatio -> Automatic, PlotPoints -> {200, 2}, 
 FrameTicks -> {Automatic, None}, PlotRangePadding -> None]

No Smearing

This involves no need for smearing in the vertical direction because it calculates the density function one-dimensionally in the first place. The methods above have their justification too, when the data list does have two-dimensional points that you want to project onto a single axis.

2 Added solution using `DensityPlot`; added 278 characters in body
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