Thank you, after making your changes "Can't use string ("StartFerrite") as an ARRAY ref while "strict refs" in use at ../../plot_TTTDIA.pl line 58" this is a reference to temp_and_starts in the following block:

    # Read the file's per-temperature data
    while(<$in>) {
        # Split on multiple spaces using regex captured matches
        my @temp_and_starts = @{$_}                              =~ /[
+^\s]+/g;
        my @last_AT_fracs   = <$in>                           =~ /[^\s
+]+/g;
        my @twenty_SFs      = (<$in> . <$in> . <$in> . <$in>) =~ /[^\s
+]+/g;
        my $max_SF          = max @twenty_SFs;

        # Build the @TTTPLOT row
        $TTTPLOT[$index]->[0] = $temp_and_starts[0];
        $TTTPLOT[$index]->[1] = $temp_and_starts[1];
        $TTTPLOT[$index]->[2] = $temp_and_starts[2];
        $TTTPLOT[$index]->[3] = $temp_and_starts[3];
        $TTTPLOT[$index]->[4] = $max_SF;
        push @{ $TTTPLOT[$index] }, @twenty_SFs;
        $index++;
    }
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Is this a simple fix or does it require an overhaul?

Are you sure this has ever worked? This line makes no sense:

my @temp_and_starts = @{$_} =~ /[^\s]+/g;
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Under warnings, it even warns:

Applying pattern match (m//) to @array will act on scalar(@array)
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map{substr$_->[0],$_->[1]||0,1}[\*||{},3],[[]],[ref qr-1,-,-1],[{}],[sub{}^*ARGV,3]

Without knowing what the data looks like, here is my guess at what "should" work:

        my @temp_and_starts =  $_=~/(\S+)/g;
        my @last_AT_fracs   =  scalar(<$in>)  =~/(\S+)/g;
        my @twenty_SFs      = (<$in> . <$in> . <$in> . <$in>) =~/(\S+)
+/sg;
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                "The difficult we do today; the impossible takes a little longer."

I thought that required brackets as in my @temp_and_starts = ($_=~/(\S+)/g); but it does not.