It depends on how you define the Gospel of Thomas. Some sayings in Thomas look really late, but it also contains some sayings that are more primitive and more "difficult" than the synoptics, indicating an earlier tradition. For example, Th 71, "I will destroy this house and no one will be able to rebuild it." It lacks any apologetic or correction about rebuilding it or rebuilding it with his body. Mark just denies that Jesus threatened to destroy the Temple at all and says the witnesses were lying. So you can see the trajectory of "He said he would destroy the Temple," to "No he didn't. The witnesses were lying." 'O.K. he did, but he said he was going to build it back up again." "He meant he would build it with his body" (by the way, the Essenes used that same language about replacing the Temple with their "body."), "He said he would build a Temple not made with hands," etc. The saying as it appears in Thomas 71 is unapologetic and unqualified. i.e. more "difficult." What would be the reason for making the saying harsher and more difficult? I agree with Crossan here that this version of the saying looks earlier than the Synoptics.
Thomas is a stratified work like the Q source, though. It kept getting added to over time. Some of the sayings look really early, some look really late. The dating of GTh, as we receive it, is what it looked like in the late 2nd or early 3rd Century, but the earliest layer of sayings could be earlier than Mark or even concurrent with Q. Like Q, it lacks a resurrection and lacks any reference to Jesus as a personal savior, as divine, as a miracle worker or even as a healer. He's just a wise teacher presented in the Cynic tradition, much like the Q1 layer (in Kloppenborg's stratification), which is all wisdom teaching. It's not even apocalyptic.
Neither Q or Thomas is Aramaic, so neither goes directly back to Jesus, but some of the sayings in the earliest stratifications of Thomas and Q look like they could be differently remembered versions of a common sayings tradition.
I like Burton Mack's book on Q (The Lost Gospel: The Book of Q and Christian Origins) which argues for a scenario in which a sayings tradition attributed to Jesus developed and was added to over time with the subculture of the earliest Jesus communities leading to different strands of transmission in different directions and different pivots after 70, after the delayed parousia, etc. Mack even sees Mark as containing some independent variations on Q sayings.