I've set up Mail Poet 2.5.9 on a WordPress 3.7 local test site and I've created a newsletter I've sent to my own e-mail for testing, but it does appear blank in Thunderbird (v24.0.1).
I've tested the newsletter with your http://www.mail-tester.com/ website to find out the problem and the following messages were displayed :
-2 MIME_NO_TEXT MIME_NO_TEXT
-0.001 MISSING_MIME_HB_SEP Missing blank line between MIME header and body
I've then modified line 1169 in wysija-newsletters\inc\phpmailer\class.phpmailer.php from :
$result .= $this->LE;
$result .= $this->LE.$this->LE;
With this modification the e-mail is correctly displayed in Thunderbird, although your mail tester website still shows the same messages.
Any idea what the problem is and if this quick fix is the solution ?