Under the current concept, our hero has blood that flows at very low temperatures and absorbs heat at an excruciatingly slow rate... at least in the short term, there's no measurable increase in temperature at all under normal climate conditions. Her power is to pull heat into herself, freezing objects around her, and dumping that heat energy into her blood as a "heat sink." Coldblooded on an extreme scale.
Now, I'm probably going to handwave the mechanics of her pulling the heat in from specific locations. But I'm trying to think about how the blood itself would work. What kind of real-world substances could it be made of? How would it move oxygen around? (I've got this vague idea of it actually condensing the oxygen into liquid form and letting it flow that way, but I'm not sure if the cells could take it in that form, even if they evaporate it again first.) Could this blood still clot properly, and how? What other purposes of blood might be complicated by these temperatures or substances? What would these temperatures do to the rest of her body, and how might she, or her cells, have adapted to handle this problem? (Another vague idea I have is that she has to draw heat regularly to keep her body from going cryogenic.)
EDIT: My physics are admittedly rusty, so apparently my explanation wasn't clearly worded. What I wanted to say was that her blood has a gargantuan specific heat capacity. The same amount of heat energy that it would take to freeze, say, a bathtub full of hot water would raise her blood temperature maybe a millionth of a Kelvin, if that. I'm going to avoid putting an actual number on it, but hopefully you get the idea; in laymen's terms, her blood is just really, really stubborn about warming up.