In approaching the concept of neutrality in pH and the Orwellian double-think involved in discussing H+ while simultaneously not believing in its existence, a non-specialist relies on the guidance of a serious chemistry expert. Specifically, the expertise of such a chemist must be specifically in the behaviour and properties of water. No single source has greater detail or more lucid explanations for this topic than Prof. Martin Chaplin, in his site "Water Structure and Science". Specifically, the reader is invited to review the chapter on "Water dissociation and pH", which deals with the autoionisation of water, and which is critical to the understanding of pH as a whole.

The dissociation constant of something that is not supposed to dissociate

Even though generally chemistry people acknowledge the fact that there really is no such thing as a free-range hydrogen ion, the very same people will also be observed to discuss Kw, the ionisation constant of water which depends for its existence on the following equilibrium:

H2O ⇌  H+ + OH- 

Thus,

Kw = [H+][OH-]

As already mentioned elsewhere, rather than discussing naked H+ ions we should probably be discussing aH+ which is the activity of those ions, or at least H3O+.

To satisfy the proton Nazis, we should rewrite the equation in the following fashion:

2H2O(aq)  ⇌ H3O+(aq) + OH-(aq)

Thus,

Kw = [H3O+][OH-]

The endothermic autoionisation of water

The reaction which creates H3O+ and OH- is an endothermic reaction. Energy is absorbed by the progress of the reaction to the right; or, put another way, heat energy violently breaks the H2O molecule into its ionised components.

How much energy is required for this? Reliable sources report that in a hard vacuum, the act of destroying a water molecule is extremely energy-expensive - requiring 1.66 MJ per mole of water. Comparatively, the aqueous dissociation of ions is much more gentle, requiring about a third of this energy.

In any case, the interaction of H2O,  H3O+ and OH- is a dynamic equilibrium. The addition of heat energy into the equation pushes the reaction further to the right, driven by the relentless Le Châtelier's Principle.

The more heat is available in the system, the more the system will trend towards autoionisation of the molecules. Conversely, as heat is removed from the system by cooling, so the ions will reunite and become well-behaved water molecules again.

Thus, temperature changes will change the proportion of H3O+ and OH- to H2O. Specifically, the concentration of H3O+ will change, and we are interested in this because it is our convenient surrogate for aH+, the activity of hydrogen which we measure with our pH sensitive electrodes.

Changes in pH associated with the change of temperature and pressure

A change in concentration/activity of H3O+ is a change in pH because pH is the negative log10 of this concentration/activity. Thus, with changes in temperature, the pH of any solution will change.

In fact, at -35 C° the pH of pure distilled water is measured as 8.5.

At 0 C°, the neutral pH is 7.5. For every 1 degree increase, the neutral pH decreases by about 0.017, but this relationship is this linear only in the vaguely human-life-sustaining range of temperatures.

At 300 C° the pH is 6.0. Of course, it is hard to take that number too seriously, because some bizarre ionization behaviours are observed when one is dealing with water at that temperature. For one, it maintains its state as a liquid only at a pressure of about 50 MPa (fifty megapascals; that is about 500 atmospheres). To explore this weird territory further, we can refer to the experiments by Bandura and Lvov, who published their report on the ionisation constant (Kw) of water over a range of temperatures and pressures up to 800 C° and 100MPa. These brave men in turn refer to an even earlier experiment by Holzapfel and Franck, which is not available among the online literature, and which involved water at 1000 C° and 10,000 MPa (about 98,600 atmospheres of pressure, which is well on the way towards metallic hydrogen).

It is difficult to reconcile that sort of scenario with anything clinically familiar; the enraged steam demon in that platinum crucible does not resemble anything you would immediately recognise as water. Because most intensive care staff will never have to interpret the pH of supercritical fluids, I will abort this digression here.

Suffice to say, pH increases with a decrease in temperature, and vice versa.

If berserk changes in temperature are clinically irrelevant, then berserk changes in pressure are doubly so, and it is only in passing I mention that Kw is roughly doubled at 100 Mpa. At pressure changes which are survivable by humans (i.e. ones not measured in megapascals) the pH of body fluids will not be significantly altered.

The pH of neutrality

As temperature changes, the notional pH measurement of any solution drifts up and down. Among the lay, this may give rise to the impression that the acidity of the solution is changing. The pH is 7.5, they might say. The patient is alkalotic, etc etc.

This misconception arises from a failure to understand the modern definition of pH, and from people's inappropriate attachment to the number 7.

Indeed, a pH of 7 describes neutrality; however this is only true for a specific situation: distilled water, at 760mmHg, and at 25C°. At 37C°, the pH of distilled water is actually around 6.8, which means the human extracellular fluid is quite alkaline. However, the intracellular pH of the warm-blooded human is still around 6.8. This has been confirmed by various destructive and non-destructive measurements. Indeed, for a beautifully detailed account of the tissues and experimenters who boiled mashed and electro-probed them, I direct the gentle reader to the 1981 edition of Intracellular pH, by Albert Roos and Walter F. Boron.

In short, intracellular pH resembles the pH of neutrality at body temperature, whereas the extracellular fluid is relatively alkaline.  By carefully navigating the edges of this deep rabbit hole, we may be lucky enough avoid discussions of several highly distressing issues.  For instance, if the body fluids are alkaline in reference to the pH of neutrality, then is there really any such thing as acidaemia and acidosis? 

...Nevermind.

References

Device-specific information in all these ABG pages refers to the ABG machine used in my home unit.

Other machines may have different reference ranges and different symbols.

For my ABG analyser, one can examine this handy operations manual.

There is also an even more handy reference manual, but one needs to be an owner of this equipment before one can get hold of it. Its called the "989-963I ABL800 Reference Manual" and can occasionally be browsed accidentally.

Covington, Arthur K., R. G. Bates, and R. A. Durst. "Definition of pH scales, standard reference values, measurement of pH and related terminology (Recommendations 1984)." Pure and Applied Chemistry 57.3 (1985): 531-542.

Reed, Christopher A. "Myths about the Proton. The Nature of H+ in Condensed Media." Accounts of chemical research 46.11 (2013): 2567-2575.

Palascak, Matthew W., and George C. Shields. "Accurate experimental values for the free energies of hydration of H+, OH-, and H3O+." The Journal of Physical Chemistry A 108.16 (2004): 3692-3694.

Franks, Felix. Water: a matrix of life. Vol. 22. Royal Society of Chemistry, 2000.

Yagasaki, Takuma, et al. "A theoretical study on anomalous temperature dependence of pKw of water." The Journal of chemical physics 122.14 (2005): 144504.

Ohtaki, Hitoshi. "Effects of temperature and pressure on hydrogen bonds in water and in formamide." Journal of molecular liquids 103 (2003): 3-13.

Bandura, Andrei V., and Serguei N. Lvov. "The ionization constant of water over wide ranges of temperature and density." Journal of Physical and Chemical Reference Data 35.1 (2006): 15-30.

Moon, Richard B., and John H. Richards. "Determination of intracellular pH by 31P magnetic resonance." Journal of Biological Chemistry 248.20 (1973): 7276-7278.

Roos, Albert, and Walter F. Boron. Intracellular pH. American Physiological Society, 1981.'