When the body temperature drops, this has the effect of reducing the potential across the axonal membrane slightly. At a body temperature of 30°C,...

(a) If instead of a human neuron we had just a random lipid bilayer and some sodium ions, we would expect that the difference in electrical potential from having more ions outside than inside would lead to a positive charge outside and a negative charge inside, thus causing sodium ions to migrate inward until the potential difference was canceled out. Thus, from pure physics, we would assume that the outside concentration and the inside concentration...

(a) If instead of a human neuron we had just a random lipid bilayer and some sodium ions, we would expect that the difference in electrical potential from having more ions outside than inside would lead to a positive charge outside and a negative charge inside, thus causing sodium ions to migrate inward until the potential difference was canceled out. Thus, from pure physics, we would assume that the outside concentration and the inside concentration are the same, at 10^18 ions per cubic centimeter.

(b) Since the experimentally measured concentration of ions is about 16 times larger than what the physical equilibrium would predict, something has to be breaking that equilibrium. Some mechanism has to be resisting the effect of the electrical charge difference and forcing sodium ions to go outside even when electrostatic force is trying to pull them inward.

What is doing this in the neuron? Ion pumps. They're pretty much what they sound like: Very tiny pumps made of proteins that pass through the cell membrane of the neuron and actively catalyze reactions that pull ions from inside the cell to outside the cell or vice-versa. In this case, the sodium ion pumps must be pushing the sodium ions outside in order to maintain the high outside concentration.

(c) In a state of disease, something could go wrong with the ion pumps. Various things could happen to damage the neuron or even kill it outright, which would stop the ion pumps from functioning and thereby allow the ions to return to equilibrium.

(d) There are all sorts of nasty diseases one can get from failed ion channels, ranging from epilepsy to kidney failure. The nervous system is absolutely vital for the functioning of the rest of the body, and ion pumps are absolutely vital for the functioning of the nervous system. I've linked some medical resources that offer more details on what can happen if your sodium channels go bad.