Provided you also provide the year, it is easy:

use Time::Local;

my $timestring='Thu Jan 8 07:01:01';

my (undef,$mon,$mday,$hour,$min, $sec)=split / |:/, $timestring;
my $year=2004;

my $time = timelocal($sec,$min,$hour,$mday,$mon,$year);

print "$timestring = $time = " . scalar(localtime($time));
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