It seems like none of the answers I see up to now are actually producing heat maps. The difference between a heat map and a `ListDensityPlot` is important. In _Mathematica_ vocabulary, the heat map is a `SmoothDensityHistogram`.

First of all, I tried to _directly_ use the 'heatMap' function in [my answer][1]. I just tried it with the data in that post:

    data = RandomReal[1, {100, 2}];
    
    Show[heatMap[data, "Points" -> 300, "Radius" -> {10, .02}, 
      PlotRange -> {{0, 1}, {0, 1}}, 
      ColorFunction -> ColorData["Rainbow"]], Graphics[Point@data], 
     PlotRange -> {{0, 1}, {0, 1}}]

![smearedsquare][2]

All I did is to specify a _tuple_ `{10, .02}` for the `"Radius"` option. Its first entry is the radius in the vertical direction, and with a choice of `10` this smears all the data out over the entire vertical image range. 

This shows it works without modifying the code. But of course I have to tweak the function in order to make it look more "one-dimensional":

    heatMap[data_, opts : OptionsPattern[]] := 
     Module[{n, size, xRange, pr}, 
      n = "Points" /. {opts} /. {"Points" -> 100};
      pr = PlotRange /. {opts} /. {PlotRange :> 
          Map[{Min[#], Max[#]} &, Transpose[data]]};
      xRange = -Subtract @@ pr[[1]];
      size = Floor[
        n ("Radius" /. {opts} /. {"Radius" -> xRange/6})/xRange];
      Graphics[
       {Inset[
         ArrayPlot[
          Rescale@GaussianFilter[
            ImageData@ColorNegate@ColorConvert[
               Rasterize[
                Graphics[
                 Point[data],
                 Background -> White,
                 PlotRangePadding -> 0,
                 ImagePadding -> 0,
                 ImageMargins -> 0,
                 PlotRange -> pr
                 ],
                "Image",
                ImageSize -> n
                ],
               "GrayScale"
               ],
            {3 size, size},
            Padding -> 0
            ],
          ColorFunction -> (ColorFunction /. {opts} /. {ColorFunction -> 
               ColorData["LakeColors"]}),
          ImagePadding -> 0,
          PlotRangePadding -> 0,
          Frame -> False
          ],
         pr[[All, 1]],
         {0, 0}, xRange]},
       PlotRange -> pr,
       Frame -> True,
       FrameTicks -> {Automatic, None}
       ]
      ]

So here I removed the `PlotRangePadding` and the `FrameTicks` on the left side, as well as the `PlotRangePadding`. I think that's all you need to change. Having collapsed the `data` onto a single axis, the vertical smearing for `GaussianFilter` needs to be only of order `1` (in relation to the horizontal axis) - so that's what I used. Then I set the `PlotRange` appropriately and get this:

    data = RandomReal[{0, 1}, 100];
    data = {#, 0} & /@ data;

    heatMap[data, "Points" -> 300, "Radius" -> {1, .02}, 
     PlotRange -> {{0, 1}, {0, .04}}, PlotRangePadding -> 0, 
     FrameLabel -> None]

![heatmapThin][3]

The meaning of the option `"Points"` (number of horizontal sampling points) is the same as described in the linked post.

**Edit**

As I mentioned, a heat map is also realizable using built-in smoothed histogram techniques. I think the easiest way to do that in the present case would be as follows:

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

![heatmapDensityPlot][4]

The unequal smearing is now achieved by specifying a _tuple_ for the "bandwidth" parameter in `SmoothKernelDistribution`: in `{1, .02}`, the `1` is again chosen to be large compared to the plot range in the `y` direction (from `0` to `.2`) so that you get vertical bands. It's of also necessary to adjust the number of `PlotPoints` to be large enough in the horizontal direction so as to capture all the details of the distribution. The vertical number of `PlotPoints` (the second number in `{200, 2}`) can be set to the smallest possible value, `2`.

**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][5]

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 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][6]

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

  [1]: http://mathematica.stackexchange.com/a/6082/245
  [2]: http://i.stack.imgur.com/fIo5b.png
  [3]: http://i.stack.imgur.com/phRlQ.png
  [4]: http://i.stack.imgur.com/GSiVz.png
  [5]: http://i.stack.imgur.com/sZHM3.png
  [6]: http://i.stack.imgur.com/lRJtP.png