use strict;
my @file = qw(file1.txt file2.txt file3.txt);

# read all files into one big 3D matrix
my $data = [];
for my $i (0 .. $#file) {
  open DATA, '<', $file[$i] or die;
  while (<DATA>) {
    chomp;
    my @line = split /\s+/, $_;
    my $linenum = shift @line;
    $data->[$_][$linenum][$i] = shift @line for (0..$#line);
  }  
}

# output to files for each variable
for my $n (0 .. $#$data) {
  open FILE, '>', "var$n.txt" or die;
  select FILE;
  for my $linenum (0 .. $#{$data->[$n]}) {
    print join "\t", $linenum, @{$data->[$n][$linenum]}, "\n";
  }
  close FILE;
}
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I fed the above code with file1.txt, file2.txt, and file3.txt all identical to the file below:

0 0 1 2 3 4 5
1 0 1 2 3 4 5
2 0 1 2 3 4 5
[download]

Which then produced the following files:

0    0    0    0    
1    0    0    0    
2    0    0    0
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0    1    1    1    
1    1    1    1    
2    1    1    1
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0    2    2    2    
1    2    2    2    
2    2    2    2
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0    3    3    3    
1    3    3    3    
2    3    3    3
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0    4    4    4    
1    4    4    4    
2    4    4    4
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0    5    5    5    
1    5    5    5    
2    5    5    5
[download]

I'm sure that there might be a more memory efficient method, perhaps using PDL. However, if your files are not extremely large, then you should be fine.