Is change of pH of water with respect to temperature linear?
To summarize... in aqueous solutions:


Basic means $\ce{[OH−] &gt; [H+]}$
Acidic means that $\ce{[H+] &gt; [OH-]}$
Neutral means $\ce{[OH−] = [H+]}$


There is a for the Wikipedia article for the autodissociation of water. The  chemical equation for the autodissociation is:
$$\ce{H2O &lt;=&gt; H^+ + OH^-}$$
The mathematical relationship between $K_d^t$, $\ce{[H^+]}$, $\ce{[OH^-]}$ and $t$ is: $$K_d^t =\ce{[H+][OH-]}\quad\text{for }t &gt; 32\text{ C}$$
Note that $K_d^t$ changes with temperature $t$, but for pure water at any temperature, $t$,  the water will be neutral, and $\ce{[OH−] = [H+]}$. The temperature dependency of $K_d^t$ also means that pH + pOH is not always 14. 

The Wikipedia article shows that the relationship between $K_d^t$ and temperature is a curve. (The curve shown is a bit odd in that water boils at 100 C, so higher temperatures must be taken under pressure.) 

Also regardless of temperature the $\text{pH}$ of an aqueous solution is defined as $\text{pH} = -\log{\ce{[H^+]}}$ so the pH does not depend on $\ce{[OH^-]}$.