How to create matrix/mesh plot of data table properly?

This is the simplified version of this question. While the other question contains raw data consisting of real dates, in this question I have converted the raw dates to decimal date values (unit: hours) in the very first column.

Consider the following Minimum Working Example (MWE):

\documentclass[tikz]{standalone}
\usepackage{pgfplots, filecontents}

\begin{filecontents*}{data.dat}
0.000 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 2   2
0.083 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 3   3
0.167 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 4   4
0.250 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 5   5
0.333 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 6   6
0.417 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 7   7
0.500 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 8   8
0.583 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 9   9
0.667 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 10  10
0.750 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 11  11
\end{filecontents*}

\begin{document}

\begin{tikzpicture}
\begin{axis}[view={0}{90}]
\addplot3[surf, mesh/cols=10] table {data.dat};
\end{axis}
\end{tikzpicture}

\end{document}

Explanation of the table: First column serves the date as decimal_date (unit: hours), rest of the table is y-columns including a z-value in each cell for each heatmap coordinate. Furthermore, the column index numbers from 1 to 10 also provide the real index numbers of each column in reality. For example, with 10 columns, the y-values of the heatmap would go from 1 to 10.

Screenshot of the result: How do I have to configure the plot to get the following behavior:

• first column of data table (decimal hours) should provide x-axis values (= 10 pcs)
• index numbers of columns should provide y-axis values (= 10 pcs)
• cell values should provide corresponding heatmap coordinate values (= 100 pcs)

In the end it should look like this (no colorbar required): • Is your data whitespace-delimited? In the other question, the data has semicolons. In my answer, each line of a file is splitted at whitespaces with the line for v in string.gmatch(line, "%S+") do. The %S would need to be replaced appropriately for other delimiters (which should of course not occur in the data items) – Faekynn Aug 3 at 21:21

Basically, this seems to be the problem of reordering the matrix data into a vector. The easiest solution is certainly to save the data in a format suitable for pgfplots. But it is also possible to reorder the data with the help of a lua script. I have adapted another answer of mine tackling the same problem, but with a slightly different data structure.

\documentclass[tikz]{standalone}
\usepackage{pgfplots,filecontents,luacode}
\pgfplotsset{compat=1.16}

\begin{filecontents*}{data.dat}
0.000 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 2   2
0.083 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 3   3
0.167 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 4   4
0.250 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 5   5
0.333 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 6   6
0.417 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 7   7
0.500 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 8   8
0.583 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 9   9
0.667 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 10  10
0.750 0.083   0.25    0.25    0.2 0.22    0.45    0.6 0.5 11  11
\end{filecontents*}

\begin{filecontents}{mat-rewrite.lua}
\begin{luacode}

function rewrite_mat(infilename, outfilename)
infile  = io.open( infilename, "r")
outfile = io.open(outfilename, "w")

ynum = 0
xnum = 0
yvals={}
xvals={}
zvals={}

for line in infile:lines() do
t={}                               -- make a table from the line (whitespace-delimited)
length=0
for v in string.gmatch(line, "%S+") do
length = length + 1
t[length]=v
end

if ynum == 0 then
ynum = length - 1
end

xnum = xnum + 1                    -- count number of x values

xvals[xnum]=t                 -- all other lines: store x and z values
for y=1,ynum do
index = ynum*(xnum-1)+y
zvals[index]=t[y+1]
end
end

infile:close()
--znum = xnum * ynum  -- not needed

for x = 1,xnum do
for y = 1,ynum do
-- commented debug output
--tex.print(xvals[x], yvals[y], zvals[(x-1)*ynum+y],"")
--print(xvals[x], yvals[y], zvals[(x-1)*ynum+y],"")
outfile:write(xvals[x] .. " " .. y .. " " .. zvals[(x-1)*ynum+y] .. " " .. "\string\n")
end
end

outfile:close()

end
\end{luacode}
\end{filecontents}
\input{mat-rewrite.lua}
% run function mat-in.txt for structure, mat-in2 for matrix with values

\begin{document}
\directlua{rewrite_mat("data.dat","out.txt")}
\begin{tikzpicture}
\begin{axis}[mesh/ordering=y varies, unbounded coords=jump,colorbar,title={data from infrared measurements},view={0}{90},xlabel=$x$,ylabel=$y$,colorbar style={xlabel=$^\circ\mathrm{C}$,xticklabel pos=upper,xlabel style={yshift=.22cm}}] 