Now, with that disclaimer out of the way...
God is absolutely simple: he is not a composite being possessed of anything that might be construed as "parts". This is no new idea with St. Thomas; it is discussed by St. Augustine in De Trinitate VI (it might be worth noting that the New Advent page to which I'll be linking preserves an apparent typo in the edition of ST that they use; it refers to Book IV of De Trinitate for a quotation used by Aquinas, but it seems that it should have been Book VI: a simple transposition).
The absolute simplicity of God may be shown in many ways.By way of observation on just one of the implications of this: we must understand all passages of the Scripture which speak of God's "wrath" as speaking figuratively. For if our actions can really cause God to become angry, then he stands in some sort of potentiality towards the creation, so that our actions would constitute a cause eliciting an effect in God - to make him angry. But that is absurd. So we have be cautious in what we attribute to God from our reading of the Bible.
First, from the previous articles of this question. For there is neither composition of quantitative parts in God, since He is not a body; nor composition of matter and form; nor does His nature differ from His "suppositum"; nor His essence from His existence; neither is there in Him composition of genus and difference, nor of subject and accident. Therefore, it is clear that God is nowise composite, but is altogether simple.
Secondly, because every composite is posterior to its component parts, and is dependent on them; but God is the first being, as shown above (2, 3).
Thirdly, because every composite has a cause, for things in themselves different cannot unite unless something causes them to unite. But God is uncaused, as shown above (2, 3), since He is the first efficient cause.
Fourthly, because in every composite there must be potentiality and actuality; but this does not apply to God; for either one of the parts actuates another, or at least all the parts are potential to the whole (ST Q3 A7).