If it's a special run, you can just redirect (./foo 2> /path/to/testlog.txt) from the command line. Otherwise,

open local(*STDERR), '>>', '/path/to/testlog.txt' or die $!
    if $TESTING;
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You can remove the "if $TESTING" clause if you want to log all errors from this code. If you do that, you may want to include a timestamp in your warnings and dying words.