It appears to me that your datafiles have a hierarchical structure. So you'll have to parse them, and I think, for a generic parsing routine (now you only have to merge the files, but I'm sure that later on you'll have to write a similar script to do other stuff to the same files), it makes the most sense to parse the data into a data structure (a tree); see perldsc and perllol to see what kind of stuff I'm talking about.

Load all datafiles in a proper manner into the same data structure.

As a second step, you'll have to produce the desired output from the produced tree.

Step 1: load the data from all files into a data structure:

my @files = qw(File1.txt File2.txt);
my %tree;
my(@iterations, @names);  # order
foreach my $file (qw(File1.txt File2.txt)) {
    open my $fh, '<', $file or die "Cannot open file $file: $!";
    (my $name = $file) =~ s/\.\w+$//;  # remove extension
    push @refs, $ref;  # order
    my($iteration);
    while(<$fh>) {
        chomp;
        if(/^Iteration /) {
            $iteration = $_;
            push @iterations, $iteration unless $tree{$iteration};  # 
+key order
        } elsif(my($i) = /^(\d+):/) {
            $tree{$iteration}[$i]{$name} = $_;
        }
    }
}
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You can show the contents of the data structure, to see if it works:

use Data::Dumper;
print Dumper \%tree;
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Step 1 is done. Now step 2: print out the data to a file.

foreach my $iteration (@iterations) {
    print "$iteration\n";  # section header
    my $section = $tree{$iteration};  # array ref
    for my $i (0 .. $#$section) {
        my @data;
        foreach my $name (@names) {
            my $data = $section->[$i]{$name};
            next unless defined $data;
            push @data, "$name:$data";
        }
        if(@data) {
            my $line = join " ", @data;
            print "$line\n";
        }
    }
}
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I think that rounds it up...