How to fix that?

Don't use yield:

threads->yield();
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That effectively equates to sleep( 0 ), which whilst it ensures that other threads get a timeslice, equates to:

saveThreadContext;
restoreThreadContext;
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when there are no other threads available to run; which is a cpu costly way to implement a delay.

Replace it with Win32::Sleep( 33 ) will ensure that the gui remains responsive at speed faster than the eye can detect, but will drop the cpu usage of that thread to near 0.

Which translates into what linechanges in OPs code?

Should be as simple as:

#######my $DataQueue = Thread::Queue->new();
...
#wait for data, print data to GUI textbox
#######while(Win32::GUI::DoEvents() != -1) {
#######    my $tmptxt = $DataQueue->dequeue();
#######    $main_text_window->Append($tmptxt);
#######}

Win32::GUI::Dialog();

sub mainloop {
    while (1) {
        #lots of page getting and number crunching goes here
##########        $DataQueue->enqueue("some data");
        $main_text_window->Append($tmptxt);
    }
}
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Though that is untested.