But it's possible to ask, what can we change if we can change brain, conditional on the fixed IQ score. But then the "free will" intuition collapses; it's hard to imagine what we could change if our thought processes were restricted in some weird way.
Most people realize they don't have the brainpower to be the next Einstein. On the contrary, the general population has a phobia of anything involving math. I don't think this imposes much of an obstacle against free will. If you restrict to the "It's not exactly rocket science" domain, there are still plenty of choices to be made.
It's true that one can measure his IQ, and that IQ rarely changes much, but still: if you consider IQ fixed and external factor out of your control, then you must consider your thought processes restricted to some set and therefore, not totally under your control.
There are plenty of things restricting my thought processes. There are memory and speed limitations. There's my upbringing and cultural norms. I know my thinking to be prone to error. Free will isn't about being completely free of all constraints. Our courts already apply a "reasonable person" test where they examine what a rational person with ordinary intellectual capabilities could be expected to do. Limits to one's mental abilities have always been accepted along with free will. In fact, most Christian free-will apologists would consider it outright blasphemous to suggest perfect reasoning ability.
This is a sort-of response to this post.
"Things under your control" (more generally, free will) is an ill-defined concept: you are an entity within physics; all of your actions and thoughts are fully determined by physical processes in your brain. Here, I will assume that "things under your control" are any things that are controlled by your brain, since it is a consistent definition, and it's what people usually mean when they talk about things under one's control.
So, you may be interested in the question: how much one's success depends on his thoughts and actions (i.e. things that are controlled by his brain) vs. how it depends on the circumstances/environment (i.e. things that aren't)? Another formulation: how you can change one's life outcomes if you could alter neural signals emitted by his brain?
We also could draw the borderline somewhere else; maybe add physical traits, like height or attractiveness to the "internal factors" category, or maybe assign some brain parts to the "external factors" category. The question whether your life success is mostly determined by "internal factors" or "external factors" would remain valid -- and we call it "internal vs. external locus of control" question.
But what happens when we assign IQ to the "external factors" category?
IQ test is an attempt to measure some value, which is supposed to be a measure of something like quality of one's thinking process. So, this value can be seen as a function IQ(brain), which maps brains to numbers. Your thoughts and actions don't depend on your IQ score; IQ score depends on your thoughts. That's how the causal arrows are arranged.
But it's possible to ask, what can we change if we can change brain, conditional on the fixed IQ score. But then the "free will" intuition collapses; it's hard to imagine what we could change if our thought processes were restricted in some weird way. And such question is hardly practical, in my opinion. It's true that one can measure his IQ, and that IQ rarely changes much, but still: if you consider IQ fixed and external factor out of your control, then you must consider your thought processes restricted to some set and therefore, not totally under your control.
Define "things under your control" as "things under your brain neural signals' control", and then we will have a consistent definition, and we will find ourselves in the common sense domain. Declare that everything is under control of physics, and then we will, again, have a consistent definition of "things under your control" (empty set), and now we are in the physics domain. Both cases are quite intuitive.
But when we consider IQ external, "things under your control" are your thoughts, but not quite; we can control our thoughts, but only as long as they reside on some weird manifold of thought-space. I guess that in such case, your "free will" intuitions would be disrupted. Basically, we can't slice some part of what we call "personality" out and still have our intuitions about personality and free will sane.
TL; DR: You shouldn't consider any functions of your current brain state as external when discussing locus of control, since such viewpoint is actually counterintuitive and, therefore, makes you prone to errors.