Many scholars think that the Gospel of Thomas reflects A) the Q tradition and B) only proto-Gnostic ideologies at best.

It is hard to say for sure, just because of how little we have of Gnostic literature in general. The other problem is that their cosmology can actually be difficult to reconstruct entirely, since Gnosticism wasn’t one unified group. For example there were differences between Gnostics who were dualists and Valentinian Gnostics who had a form of monism.

It is particularly hard to know what really early Gnostics believed and practiced, since they are primarily only recorded by biased church fathers. The Nag Hammadi texts date to around the 3rd and 4th centuries.

While I’d love to see what you do as well, I think it may have to wait until we can get more information, if we can, since we simply have far too limited a corpus, which definitely doesn’t reflect the views of all Gnostic sects, and it is unknown if they reflect the early ones at all.

At best the Gospel of Thomas would reflect some proto Gnostic beliefs, possibly, but this isn’t known for sure, and I know of many scholars who contend that it isn’t Gnostic at all.

Critics generally dismiss the notion that the Gospel of Thomas is Gnostic primarily because there isn’t very much textual basis for such. The sayings it presents[1] cannot be said to be clear cut, absolute, Gnostic in any way (in fact they barely resemble anything Gnostic). A major problem is that the Gospel of Thomas does not condone nor deny the divinity of Jesus. So it is neither pro or con in regards to Gnostic teachings.

Critics of the proto-Gnostic generally regard it as an early Christian writing, more or less representing the Q Tradition, as structurally  and textually it shares quite a lot with Q, and Matthew and Luke, and even some similarities with Mark. Another issue that is generally raised is that the Gnostic relation is often regarded as a result of it being found among other Gnostic texts (Nag Hammadi).

The reality is that I don’t think that a compelling argument can yet be made as to its originators.
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1. For a translation of the Gospel of Thomas see: ** you do not have permission to see this link **

Because it structurally conforms to Q (being a collection of sayings, with no set narrative, which should be reflected if it was based on the synoptic tradition). The paralleled logia in Q are not direct copies of those in the synoptics, further implying that they are from an earlier source shared by both. 

Ehrman however is of the opinion that Thomas is not synoptic but Gnostic, because it lacks apocalyptic themes, which was characteristic of Jesus’ ministry.

Robert said

Chris_Hansen said
Because it structurally conforms to Q (being a collection of sayings, with no set narrative, which should be reflected if it was based on the synoptic tradition). The paralleled logia in Q [I assume you mean Thomas here] are not direct copies of those in the synoptics, further implying that they are from an earlier source shared by both. 
Ehrman however is of the opinion that Thomas is not synoptic but Gnostic, because it lacks apocalyptic themes, which was characteristic of Jesus’ ministry.  

As a student, you will, I presume, appreciate a few corrections:

Q does contain some narrative material, eg, the temptation of Jesus (Q 4,1-4.9-12.5-8.13), the Centurion’s faith (Q 7,1.3.6b-9.10?), and the Beelzebul Accusation (Q 11,14-15.17-20, cf Q 12,10).

The question of Thomas being dependent upon or independent of the synoptic gospels is completely separate from the of issue of the sayings genre of Thomas. Thus there are scholars on both sides of the former question, eg, Ehrman (independence), Meier (dependence), etc, who agree on the genre of the sayings of Thomas.

The fact that some statements in Thomas are not direct copies of synoptic sayings does not imply they are earlier. Thomistic redaction could occur at any point in time, either before or after the writing of the synoptic gospels.

The fact that Thomas is non- and even anti-apocalyptic at points suggests a later time of composition, and therefore a greater  likelihood of dependence and a lesser likelihood of independence on the synoptic gospels.  

Should have clarified that I meant it had no overall narrative. It does, as you kindly pointed out, have narrative material, but no overall one.

And I would note that Marvin Meyer and a number of other scholars argue independence based on genre of the work. So I wouldn’t say that the genre and Dependence/Independence debate are separate (despite Casey’s complaints on the matter).