Try something like this:

#! perl -slw
use strict;
use threads;
use Thread::Queue;
use Net::FTP;

my $THREADS = 10;

my $Q = new Threads::Queue;

my @threads = map async {
    my $ftp = Net::FTP->new("host.com");
    $ftp->login('blah','blah');
    $ftp->ascii();
    while( defined( $_ = $Q->dequeue )  ) {
        $ftp->put( $_ );
    }
    $ftp->quit();
},  1 .. $THREADS;

my @files = getFiles();

$Q->enqueue( @files );
$Q->engueue( (undef) x $THREADS );

$_->join for @threads;
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Start with small values (eg.10) for $THREADS and see how things go. Adjust higher slowly.