Like for instance, Sola Scriptura is heresy, but there's no logical inconsistency between believing in sola scriptura, and believing in God.  

There's no logical inconsistency between believing in evolution and the Big Bang, and believing in God.  Whether those former two beliefs are also heresies is what I'm trying to figure out.  I don't see how they could be heretical.  

Which is a separate question from whether or not its true.

What I mean is this.
At a strict, logical level, this is true.  There is no inconsistency between believing in a Creator, and believing that said Creator used evolution and the Big Bang to create the world.

That's a separate question than whether God did in fact do this, and whether the belief that God did this is a belief that an orthodox Catholic can hold.  Most of the answers to me have addressed that first question, but I've really been asking about the second one.

But EVEN IF it was a heresy to believe in evolution and the Big Bang, that would just make it a heretical belief, it wouldn't mean that it was inconsistent with theism.

God did not create the sun and stars until AFTER He fashioned the earth ... and plants.  That is simply not consistent with Big Bang.

An overly literalistic reading of the sun being created after the light does not make sense. God called the light day and the darkness night, before he created the Earth and before he created the Sun. What exactly would this day look like then? Half the sky being light and half the sky(or heavens rather, as the sky hadn't even been created yet) dark, with it rotating 360 degrees every 24 hours? Then it says the stars God just created separated the days from the nights, the previous separation seeming to have been undone. Referring to the Moon as a "light" would also imply it was luminescent if taken purely literally.

Hi ByzCat. You may like this article, why Human Evolution can never become part of the Deposit of Faith : http://www.theotokos.org.uk/pages/creation/cbutel/humanevo.html

An excerpt: The Magisterium Teachings of Pius IX, Leo XIII and Pius X

Pius IX. The year after the publication of Darwin’s evolution thesis, the Provincial Council of Cologne issued the following canon, which was approved by Pope Pius IX:“Our first parents were immediately created by God (Gen.2.7). Therefore we declare as quite contrary to Holy Scripture and the Faith the opinion of those who dare to assert that man, in respect of the body, is derived by spontaneous transformation from an imperfect nature, which improved continually until it reached the present human state.” [10]

Pius IX also approved the following teaching of the first Vatican Council :“This sole true God by His goodness and omnipotent power, not to increase His own beatitude, and not to add to, but to manifest His perfection by the blessings which He bestows upon creatures with most free volition, immediately from the beginning of time fashioned each creature, out of nothing, spiritual and corporeal, namely the angelic and the mundane; and then the human creation, common as it were, composed of both spirit and body.” [11] ... This part of the Vatican 1 teaching therefore cannot be reconciled with any theory of biological evolution of mundane creatures, which asserts that such life was not created immediately from the beginning of time but arose some millions or billions of years after that beginning and then only as amoeba (a unicelled organism), which then took millions of years to evolve into the kinds of living creatures specified in Genesis 1. Nor can it be said that God used an evolutionary system to create mundane creatures out of nothing."

On the whole, even Humani Generis by Pope Ven. Pius XII is very skeptical of evolution: "Some imprudently and indiscreetly hold that evolution, which has not been fully proved even in the domain of natural sciences, explains the origin of all things, and audaciously support the monistic and pantheistic opinion that the world is in continual evolution. Communists gladly subscribe to this opinion so that, when the souls of men have been deprived of every idea of a personal God, they may the more efficaciously defend and propagate their dialectical materialism. 6. Such fictitious tenets of evolution which repudiate all that is absolute, firm and immutable, have paved the way for the new erroneous philosophy which, rivaling idealism, immanentism and pragmatism, has assumed the name of existentialism, since it concerns itself only with existence of individual things and neglects all consideration of their immutable essences. 7. There is also a certain historicism, which attributing value only to the events of man's life, overthrows the foundation of all truth and absolute law, both on the level of philosophical speculations and especially to Christian dogmas ... 9. Now Catholic theologians and philosophers, whose grave duty it is to defend natural and supernatural truth and instill it in the hearts of men, cannot afford to ignore or neglect these more or less erroneous opinions." At this time, no explicit ex cathedra decision forbidding evolution to be taught has yet been made; but it's very likely one will be made by a Pope or Council in future. And one could argue Pope Bl. Pius IX and the First Vatican Council, especially in light of that 1860 Provincial Council's decision which the Pope approved, had implicitly rejected evolution in these words, "9. Hence all faithful Christians are forbidden to defend as the legitimate conclusions of science those opinions which are known to be contrary to the doctrine of faith, particularly if they have been condemned by the Church; and furthermore they are absolutely bound to hold them to be errors which wear the deceptive appearance of truth." (Vatican I Council, Session 3 : 24 April 1870, Dogmatic constitution on the Catholic Faith, Chapter 4, On Faith and Reason.)

If by "evolution of the human body" one means the evolution of the human body from an ape, I cannot see how this is not heretical.  It clearly contradicts Sacred Scripture.  It must be some amazing stretch to say that when Scripture states God created Adam's body from the "clay of the earth", that this "clay of the earth" was actually an ape.